Four bit adder

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Task
Four bit adder
You are encouraged to solve this task according to the task description, using any language you may know.
Task

"Simulate" a four-bit adder.

This design can be realized using four 1-bit full adders. Each of these 1-bit full adders can be built with two half adders and an   or   gate. ;

Finally a half adder can be made using an   xor   gate and an   and   gate.

The   xor   gate can be made using two   nots,   two   ands   and one   or.

Not,   or   and   and,   the only allowed "gates" for the task, can be "imitated" by using the bitwise operators of your language.

If there is not a bit type in your language, to be sure that the   not   does not "invert" all the other bits of the basic type   (e.g. a byte)   we are not interested in,   you can use an extra   nand   (and   then   not)   with the constant   1   on one input.

Instead of optimizing and reducing the number of gates used for the final 4-bit adder,   build it in the most straightforward way,   connecting the other "constructive blocks",   in turn made of "simpler" and "smaller" ones.

Schematics of the "constructive blocks"
(Xor gate with ANDs, ORs and NOTs)            (A half adder)                   (A full adder)                             (A 4-bit adder)        
Xor gate done with ands, ors and nots A half adder A full adder A 4-bit adder


Solutions should try to be as descriptive as possible, making it as easy as possible to identify "connections" between higher-order "blocks".

It is not mandatory to replicate the syntax of higher-order blocks in the atomic "gate" blocks, i.e. basic "gate" operations can be performed as usual bitwise operations, or they can be "wrapped" in a block in order to expose the same syntax of higher-order blocks, at implementers' choice.

To test the implementation, show the sum of two four-bit numbers (in binary).



11l

Translation of: Python
F xor(a, b)
   R (a & !b) | (b & !a)

F ha(a, b)
   R (xor(a, b), a & b)

F fa(a, b, ci)
   V (s0, c0) = ha(ci, a)
   V (s1, c1) = ha(s0, b)
   R (s1, c0 | c1)

F fa4(a, b)
   V width = 4
   V ci = [0B] * width
   V co = [0B] * width
   V s = [0B] * width
   L(i) 0 .< width
      (s[i], co[i]) = fa(a[i], b[i], I i != 0 {co[i - 1]} E 0)
   R (s, co.last)

F int2bus(n, width = 4)
   R reversed(bin(n).zfill(width)).map(c -> Int(c))

F bus2int(b)
   R sum(enumerate(b).filter2((i, bit) -> bit).map2((i, bit) -> 1 << i))

V width = 4
V tot = [0B] * (width + 1)
L(a) 0 .< 2 ^ width
   L(b) 0 .< 2 ^ width
      V (ta, tlast) = fa4(int2bus(a), int2bus(b))
      L(i) 0 .< width
         tot[i] = ta[i]
      tot[width] = tlast
      assert(a + b == bus2int(tot), ‘totals don't match: #. + #. != #.’.format(a, b, String(tot)))

Action!

DEFINE Bit="BYTE"

TYPE FourBit=[Bit b0,b1,b2,b3]

Bit FUNC Not(Bit a)
RETURN (1-a)

Bit FUNC MyXor(Bit a,b)
RETURN ((Not(a) AND b) OR (a AND Not(b)))

Bit FUNC HalfAdder(Bit a,b Bit POINTER c)
  c^=a AND b
RETURN (MyXor(a,b))

Bit FUNC FullAdder(Bit a,b,c0 Bit POINTER c)
  Bit s1,c1,s2,c2

  s1=HalfAdder(a,c0,@c1)
  s2=HalfAdder(b,s1,@c2)
  
  c^=c1 OR c2
RETURN (s2)

PROC FourBitAdder(FourBit POINTER a,b,s Bit POINTER c)
  Bit c1,c2,c3

  s.b3=FullAdder(a.b3,b.b3,0,@c3)
  s.b2=FullAdder(a.b2,b.b2,c3,@c2)
  s.b1=FullAdder(a.b1,b.b1,c2,@c1)
  s.b0=FullAdder(a.b0,b.b0,c1,c)
RETURN

PROC InitFourBit(BYTE a FourBit POINTER res)
  res.b3=a&1 a==RSH 1
  res.b2=a&1 a==RSH 1
  res.b1=a&1 a==RSH 1
  res.b0=a&1
RETURN

PROC PrintFourBit(FourBit POINTER a)
  PrintB(a.b0) PrintB(a.b1)
  PrintB(a.b2) PrintB(a.b3)
RETURN

PROC Main()
  FourBit a,b,s
  Bit c
  BYTE i,v

  FOR i=1 TO 20
  DO
    v=Rand(16) InitFourBit(v,a)
    v=Rand(16) InitFourBit(v,b)
    
    FourBitAdder(a,b,s,@c)

    PrintFourBit(a) Print(" + ")
    PrintFourBit(b) Print(" = ")
    PrintFourBit(s) Print(" Carry=")
    PrintBE(c)
  OD
RETURN
Output:

Screenshot from Atari 8-bit computer

0100 + 0000 = 0100 Carry=0
1101 + 1011 = 1000 Carry=1
1011 + 0010 = 1101 Carry=0
1101 + 0111 = 0100 Carry=1
0100 + 0101 = 1001 Carry=0
0110 + 1011 = 0001 Carry=1
1110 + 0010 = 0000 Carry=1
0010 + 1110 = 0000 Carry=1
1110 + 1110 = 1100 Carry=1
1100 + 0111 = 0011 Carry=1
0100 + 0011 = 0111 Carry=0
1101 + 0101 = 0010 Carry=1
0001 + 0011 = 0100 Carry=0
1001 + 1000 = 0001 Carry=1
1111 + 1001 = 1000 Carry=1
0001 + 0011 = 0100 Carry=0
0001 + 0000 = 0001 Carry=0
1000 + 0011 = 1011 Carry=0
1110 + 1000 = 0110 Carry=1
0010 + 0100 = 0110 Carry=0

Ada

type Four_Bits is array (1..4) of Boolean;
   
procedure Half_Adder (Input_1, Input_2 : Boolean; Output, Carry : out Boolean) is
begin
   Output := Input_1 xor Input_2;
   Carry  := Input_1 and Input_2;
end Half_Adder;

procedure Full_Adder (Input_1, Input_2 : Boolean; Output : out Boolean; Carry : in out Boolean) is
   T_1, T_2, T_3 : Boolean;
begin
   Half_Adder (Input_1, Input_2, T_1, T_2);
   Half_Adder (Carry, T_1, Output, T_3);
   Carry := T_2 or T_3;
end Full_Adder;

procedure Four_Bits_Adder (A, B : Four_Bits; C : out Four_Bits; Carry : in out Boolean) is
begin
   Full_Adder (A (4), B (4), C (4), Carry);
   Full_Adder (A (3), B (3), C (3), Carry);
   Full_Adder (A (2), B (2), C (2), Carry);
   Full_Adder (A (1), B (1), C (1), Carry);
end Four_Bits_Adder;

A test program with the above definitions

with Ada.Text_IO;  use Ada.Text_IO;

procedure Test_4_Bit_Adder is

   -- The definitions from above

   function Image (Bit : Boolean) return Character is
   begin
      if Bit then
         return '1';
      else
         return '0';
      end if;
   end Image;

   function Image (X : Four_Bits) return String is
   begin
      return Image (X (1)) & Image (X (2)) & Image (X (3)) & Image (X (4));
   end Image;

   A, B, C : Four_Bits; Carry : Boolean;
begin
   for I_1 in Boolean'Range loop
      for I_2 in Boolean'Range loop
         for I_3 in Boolean'Range loop
            for I_4 in Boolean'Range loop
               for J_1 in Boolean'Range loop
                  for J_2 in Boolean'Range loop
                     for J_3 in Boolean'Range loop
                        for J_4 in Boolean'Range loop
                           A := (I_1, I_2, I_3, I_4);
                           B := (J_1, J_2, J_3, J_4);
                           Carry := False;
                           Four_Bits_Adder (A, B, C, Carry);
                           Put_Line
                           (  Image (A)
                           &  " + "
                           &  Image (B)
                           &  " = "
                           &  Image (C)
                           &  " "
                           &  Image (Carry)
                           );
                        end loop;
                     end loop;
                  end loop;
               end loop;
            end loop;
         end loop;
      end loop;
   end loop;
end Test_4_Bit_Adder;
Output:
0000 + 0000 = 0000 0
0000 + 0001 = 0001 0
0000 + 0010 = 0010 0
0000 + 0011 = 0011 0
0000 + 0100 = 0100 0
0000 + 0101 = 0101 0
0000 + 0110 = 0110 0
0000 + 0111 = 0111 0
0000 + 1000 = 1000 0
0000 + 1001 = 1001 0
0000 + 1010 = 1010 0
0000 + 1011 = 1011 0
0000 + 1100 = 1100 0
0000 + 1101 = 1101 0
0000 + 1110 = 1110 0
0000 + 1111 = 1111 0
0001 + 0000 = 0001 0
0001 + 0001 = 0010 0
0001 + 0010 = 0011 0
0001 + 0011 = 0100 0
0001 + 0100 = 0101 0
0001 + 0101 = 0110 0
0001 + 0110 = 0111 0
0001 + 0111 = 1000 0
0001 + 1000 = 1001 0
0001 + 1001 = 1010 0
0001 + 1010 = 1011 0
0001 + 1011 = 1100 0
0001 + 1100 = 1101 0
0001 + 1101 = 1110 0
0001 + 1110 = 1111 0
0001 + 1111 = 0000 1
0010 + 0000 = 0010 0
0010 + 0001 = 0011 0
0010 + 0010 = 0100 0
0010 + 0011 = 0101 0
0010 + 0100 = 0110 0
0010 + 0101 = 0111 0
0010 + 0110 = 1000 0
0010 + 0111 = 1001 0
0010 + 1000 = 1010 0
0010 + 1001 = 1011 0
0010 + 1010 = 1100 0
0010 + 1011 = 1101 0
0010 + 1100 = 1110 0
0010 + 1101 = 1111 0
0010 + 1110 = 0000 1
0010 + 1111 = 0001 1
0011 + 0000 = 0011 0
0011 + 0001 = 0100 0
0011 + 0010 = 0101 0
0011 + 0011 = 0110 0
0011 + 0100 = 0111 0
0011 + 0101 = 1000 0
0011 + 0110 = 1001 0
0011 + 0111 = 1010 0
0011 + 1000 = 1011 0
0011 + 1001 = 1100 0
0011 + 1010 = 1101 0
0011 + 1011 = 1110 0
0011 + 1100 = 1111 0
0011 + 1101 = 0000 1
0011 + 1110 = 0001 1
0011 + 1111 = 0010 1
0100 + 0000 = 0100 0
0100 + 0001 = 0101 0
0100 + 0010 = 0110 0
0100 + 0011 = 0111 0
0100 + 0100 = 1000 0
0100 + 0101 = 1001 0
0100 + 0110 = 1010 0
0100 + 0111 = 1011 0
0100 + 1000 = 1100 0
0100 + 1001 = 1101 0
0100 + 1010 = 1110 0
0100 + 1011 = 1111 0
0100 + 1100 = 0000 1
0100 + 1101 = 0001 1
0100 + 1110 = 0010 1
0100 + 1111 = 0011 1
0101 + 0000 = 0101 0
0101 + 0001 = 0110 0
0101 + 0010 = 0111 0
0101 + 0011 = 1000 0
0101 + 0100 = 1001 0
0101 + 0101 = 1010 0
0101 + 0110 = 1011 0
0101 + 0111 = 1100 0
0101 + 1000 = 1101 0
0101 + 1001 = 1110 0
0101 + 1010 = 1111 0
0101 + 1011 = 0000 1
0101 + 1100 = 0001 1
0101 + 1101 = 0010 1
0101 + 1110 = 0011 1
0101 + 1111 = 0100 1
0110 + 0000 = 0110 0
0110 + 0001 = 0111 0
0110 + 0010 = 1000 0
0110 + 0011 = 1001 0
0110 + 0100 = 1010 0
0110 + 0101 = 1011 0
0110 + 0110 = 1100 0
0110 + 0111 = 1101 0
0110 + 1000 = 1110 0
0110 + 1001 = 1111 0
0110 + 1010 = 0000 1
0110 + 1011 = 0001 1
0110 + 1100 = 0010 1
0110 + 1101 = 0011 1
0110 + 1110 = 0100 1
0110 + 1111 = 0101 1
0111 + 0000 = 0111 0
0111 + 0001 = 1000 0
0111 + 0010 = 1001 0
0111 + 0011 = 1010 0
0111 + 0100 = 1011 0
0111 + 0101 = 1100 0
0111 + 0110 = 1101 0
0111 + 0111 = 1110 0
0111 + 1000 = 1111 0
0111 + 1001 = 0000 1
0111 + 1010 = 0001 1
0111 + 1011 = 0010 1
0111 + 1100 = 0011 1
0111 + 1101 = 0100 1
0111 + 1110 = 0101 1
0111 + 1111 = 0110 1
1000 + 0000 = 1000 0
1000 + 0001 = 1001 0
1000 + 0010 = 1010 0
1000 + 0011 = 1011 0
1000 + 0100 = 1100 0
1000 + 0101 = 1101 0
1000 + 0110 = 1110 0
1000 + 0111 = 1111 0
1000 + 1000 = 0000 1
1000 + 1001 = 0001 1
1000 + 1010 = 0010 1
1000 + 1011 = 0011 1
1000 + 1100 = 0100 1
1000 + 1101 = 0101 1
1000 + 1110 = 0110 1
1000 + 1111 = 0111 1
1001 + 0000 = 1001 0
1001 + 0001 = 1010 0
1001 + 0010 = 1011 0
1001 + 0011 = 1100 0
1001 + 0100 = 1101 0
1001 + 0101 = 1110 0
1001 + 0110 = 1111 0
1001 + 0111 = 0000 1
1001 + 1000 = 0001 1
1001 + 1001 = 0010 1
1001 + 1010 = 0011 1
1001 + 1011 = 0100 1
1001 + 1100 = 0101 1
1001 + 1101 = 0110 1
1001 + 1110 = 0111 1
1001 + 1111 = 1000 1
1010 + 0000 = 1010 0
1010 + 0001 = 1011 0
1010 + 0010 = 1100 0
1010 + 0011 = 1101 0
1010 + 0100 = 1110 0
1010 + 0101 = 1111 0
1010 + 0110 = 0000 1
1010 + 0111 = 0001 1
1010 + 1000 = 0010 1
1010 + 1001 = 0011 1
1010 + 1010 = 0100 1
1010 + 1011 = 0101 1
1010 + 1100 = 0110 1
1010 + 1101 = 0111 1
1010 + 1110 = 1000 1
1010 + 1111 = 1001 1
1011 + 0000 = 1011 0
1011 + 0001 = 1100 0
1011 + 0010 = 1101 0
1011 + 0011 = 1110 0
1011 + 0100 = 1111 0
1011 + 0101 = 0000 1
1011 + 0110 = 0001 1
1011 + 0111 = 0010 1
1011 + 1000 = 0011 1
1011 + 1001 = 0100 1
1011 + 1010 = 0101 1
1011 + 1011 = 0110 1
1011 + 1100 = 0111 1
1011 + 1101 = 1000 1
1011 + 1110 = 1001 1
1011 + 1111 = 1010 1
1100 + 0000 = 1100 0
1100 + 0001 = 1101 0
1100 + 0010 = 1110 0
1100 + 0011 = 1111 0
1100 + 0100 = 0000 1
1100 + 0101 = 0001 1
1100 + 0110 = 0010 1
1100 + 0111 = 0011 1
1100 + 1000 = 0100 1
1100 + 1001 = 0101 1
1100 + 1010 = 0110 1
1100 + 1011 = 0111 1
1100 + 1100 = 1000 1
1100 + 1101 = 1001 1
1100 + 1110 = 1010 1
1100 + 1111 = 1011 1
1101 + 0000 = 1101 0
1101 + 0001 = 1110 0
1101 + 0010 = 1111 0
1101 + 0011 = 0000 1
1101 + 0100 = 0001 1
1101 + 0101 = 0010 1
1101 + 0110 = 0011 1
1101 + 0111 = 0100 1
1101 + 1000 = 0101 1
1101 + 1001 = 0110 1
1101 + 1010 = 0111 1
1101 + 1011 = 1000 1
1101 + 1100 = 1001 1
1101 + 1101 = 1010 1
1101 + 1110 = 1011 1
1101 + 1111 = 1100 1
1110 + 0000 = 1110 0
1110 + 0001 = 1111 0
1110 + 0010 = 0000 1
1110 + 0011 = 0001 1
1110 + 0100 = 0010 1
1110 + 0101 = 0011 1
1110 + 0110 = 0100 1
1110 + 0111 = 0101 1
1110 + 1000 = 0110 1
1110 + 1001 = 0111 1
1110 + 1010 = 1000 1
1110 + 1011 = 1001 1
1110 + 1100 = 1010 1
1110 + 1101 = 1011 1
1110 + 1110 = 1100 1
1110 + 1111 = 1101 1
1111 + 0000 = 1111 0
1111 + 0001 = 0000 1
1111 + 0010 = 0001 1
1111 + 0011 = 0010 1
1111 + 0100 = 0011 1
1111 + 0101 = 0100 1
1111 + 0110 = 0101 1
1111 + 0111 = 0110 1
1111 + 1000 = 0111 1
1111 + 1001 = 1000 1
1111 + 1010 = 1001 1
1111 + 1011 = 1010 1
1111 + 1100 = 1011 1
1111 + 1101 = 1100 1
1111 + 1110 = 1101 1
1111 + 1111 = 1110 1

APL

Works with: Dyalog APL
Works with: GNU APL
⍝ Our primitive "gates" are built-in, but let's give them names
not  { ~  }   ⍝ in Dyalog these assignments can be simplified to "not ← ~", "and ← ∧", etc.
and  {    }
or  {    }
nand  {    }

⍝ Build the complex gates
xor  { ( and not ) or ( and not ) }

⍝ And the multigate components. Our bit vectors are MSB first, so for consistency
⍝ the carry bit is returned as the left result as well.
half_adder  { ( and ),  xor  } ⍝ returns carry, sum

⍝ GNU APL dfns can't have multiple statements, so the other adders are defined as tradfns
result  c_in full_adder args ; c_in; a; b; s0; c0; s1; c1
 (a b)  args
 (c0 s0)  c_in half_adder a
 (c1 s1)  s0 half_adder b
 result  (c0 or c1), s1


⍝ Finally, our four-bit adder
result  a adder4 b ; a3; a2; a1; a0; b3; b2; b1; b0; c0; s0; c1; s1; c2; s2; s3; v
 (a3 a2 a1 a0)  a
 (b3 b2 b1 b0)  b
 (c0 s0)  0 full_adder a0 b0
 (c1 s1)  c0 full_adder a1 b1
 (c2 s2)  c1 full_adder a2 b2
 (v s3)  c2 full_adder a3 b3
 result  v s3 s2 s1 s0


⍝ Add one pair of numbers and print as equation
demo  { 0,'+',,'=',{ 1,' with carry ',1 }  adder4  }

⍝ A way to generate some random numbers for our demo
randbits  { 1-?2 }

⍝ And go
{ (randbits 4) demo randbits 4   } ¨ 20
Output:
1 1 1 1 + 0 0 0 1 = 0 0 0 0  with carry  1
1 1 0 0 + 0 0 0 1 = 1 1 0 1  with carry  0
0 1 1 1 + 0 1 1 1 = 1 1 1 0  with carry  0
1 1 1 0 + 1 0 1 1 = 1 0 0 1  with carry  1
0 1 0 0 + 0 0 1 0 = 0 1 1 0  with carry  0
1 0 1 1 + 0 1 1 0 = 0 0 0 1  with carry  1
1 1 1 1 + 1 0 1 1 = 1 0 1 0  with carry  1
0 1 1 0 + 0 0 1 0 = 1 0 0 0  with carry  0
1 1 0 1 + 0 1 0 0 = 0 0 0 1  with carry  1
1 0 1 0 + 0 0 1 1 = 1 1 0 1  with carry  0
1 1 1 1 + 0 0 0 1 = 0 0 0 0  with carry  1
0 1 1 1 + 1 0 1 1 = 0 0 1 0  with carry  1
0 0 0 1 + 1 1 0 0 = 1 1 0 1  with carry  0
0 0 1 0 + 1 1 1 1 = 0 0 0 1  with carry  1
0 0 1 0 + 0 1 0 0 = 0 1 1 0  with carry  0
1 1 1 0 + 1 0 1 0 = 1 0 0 0  with carry  1
1 0 0 0 + 1 0 0 0 = 0 0 0 0  with carry  1
1 0 1 0 + 0 0 0 0 = 1 0 1 0  with carry  0
1 0 1 1 + 1 1 1 1 = 1 0 1 0  with carry  1
1 1 0 1 + 1 0 0 1 = 0 1 1 0  with carry  1

Arturo

binStringToBits: function [x][
    result: map reverse x 'i -> to :integer to :string i
    result: result ++ repeat 0 4-size result
    return result
]

bitsToBinString: function [x][
    join reverse map x 'i -> to :string i
]

fullAdder: function [a,b,c0][
    [s,c]: halfAdder c0 a
    [s,c1]: halfAdder s b
    return @[s, or c c1]
]

halfAdder: function [a,b][
    return @[xor a b, and a b]
]

fourBitAdder: function [a,b][
    aBits: binStringToBits a
    bBits: binStringToBits b

    [s0,c0]: fullAdder aBits\0 bBits\0 0
    [s1,c1]: fullAdder aBits\1 bBits\1 c0
    [s2,c2]: fullAdder aBits\2 bBits\2 c1
    [s3,c3]: fullAdder aBits\3 bBits\3 c2

    return @[
        bitsToBinString @[s0,s1,s2,s3]
        to :string c3
    ]
]

loop 0..15 'a [
    loop 0..15 'b [
        binA: (as.binary a) ++ join to [:string] repeat 0 4-size as.binary a
        binB: (as.binary b) ++ join to [:string] repeat 0 4-size as.binary b
        [sm,carry]: fourBitAdder binA binB
        print [pad to :string a 2 "+" pad to :string b 2 "=" binA "+" binB "=" "("++carry++")" sm "=" from.binary carry ++ sm]
    ]
]
Output:
 0 +  0 = 0000 + 0000 = (0) 0000 = 0 
 0 +  1 = 0000 + 1000 = (0) 1000 = 8 
 0 +  2 = 0000 + 1000 = (0) 1000 = 8 
 0 +  3 = 0000 + 1100 = (0) 1100 = 12 
 0 +  4 = 0000 + 1000 = (0) 1000 = 8 
 0 +  5 = 0000 + 1010 = (0) 1010 = 10 
 0 +  6 = 0000 + 1100 = (0) 1100 = 12 
 0 +  7 = 0000 + 1110 = (0) 1110 = 14 
 0 +  8 = 0000 + 1000 = (0) 1000 = 8 
 0 +  9 = 0000 + 1001 = (0) 1001 = 9 
 0 + 10 = 0000 + 1010 = (0) 1010 = 10 
 0 + 11 = 0000 + 1011 = (0) 1011 = 11 
 0 + 12 = 0000 + 1100 = (0) 1100 = 12 
 0 + 13 = 0000 + 1101 = (0) 1101 = 13 
 0 + 14 = 0000 + 1110 = (0) 1110 = 14 
 0 + 15 = 0000 + 1111 = (0) 1111 = 15 
 1 +  0 = 1000 + 0000 = (0) 1000 = 8 
 1 +  1 = 1000 + 1000 = (1) 0000 = 16 
 1 +  2 = 1000 + 1000 = (1) 0000 = 16 
 1 +  3 = 1000 + 1100 = (1) 0100 = 20 
 1 +  4 = 1000 + 1000 = (1) 0000 = 16 
 1 +  5 = 1000 + 1010 = (1) 0010 = 18 
 1 +  6 = 1000 + 1100 = (1) 0100 = 20 
 1 +  7 = 1000 + 1110 = (1) 0110 = 22 
 1 +  8 = 1000 + 1000 = (1) 0000 = 16 
 1 +  9 = 1000 + 1001 = (1) 0001 = 17 
 1 + 10 = 1000 + 1010 = (1) 0010 = 18 
 1 + 11 = 1000 + 1011 = (1) 0011 = 19 
 1 + 12 = 1000 + 1100 = (1) 0100 = 20 
 1 + 13 = 1000 + 1101 = (1) 0101 = 21 
 1 + 14 = 1000 + 1110 = (1) 0110 = 22 
 1 + 15 = 1000 + 1111 = (1) 0111 = 23 
 2 +  0 = 1000 + 0000 = (0) 1000 = 8 
 2 +  1 = 1000 + 1000 = (1) 0000 = 16 
 2 +  2 = 1000 + 1000 = (1) 0000 = 16 
 2 +  3 = 1000 + 1100 = (1) 0100 = 20 
 2 +  4 = 1000 + 1000 = (1) 0000 = 16 
 2 +  5 = 1000 + 1010 = (1) 0010 = 18 
 2 +  6 = 1000 + 1100 = (1) 0100 = 20 
 2 +  7 = 1000 + 1110 = (1) 0110 = 22 
 2 +  8 = 1000 + 1000 = (1) 0000 = 16 
 2 +  9 = 1000 + 1001 = (1) 0001 = 17 
 2 + 10 = 1000 + 1010 = (1) 0010 = 18 
 2 + 11 = 1000 + 1011 = (1) 0011 = 19 
 2 + 12 = 1000 + 1100 = (1) 0100 = 20 
 2 + 13 = 1000 + 1101 = (1) 0101 = 21 
 2 + 14 = 1000 + 1110 = (1) 0110 = 22 
 2 + 15 = 1000 + 1111 = (1) 0111 = 23 
 3 +  0 = 1100 + 0000 = (0) 1100 = 12 
 3 +  1 = 1100 + 1000 = (1) 0100 = 20 
 3 +  2 = 1100 + 1000 = (1) 0100 = 20 
 3 +  3 = 1100 + 1100 = (1) 1000 = 24 
 3 +  4 = 1100 + 1000 = (1) 0100 = 20 
 3 +  5 = 1100 + 1010 = (1) 0110 = 22 
 3 +  6 = 1100 + 1100 = (1) 1000 = 24 
 3 +  7 = 1100 + 1110 = (1) 1010 = 26 
 3 +  8 = 1100 + 1000 = (1) 0100 = 20 
 3 +  9 = 1100 + 1001 = (1) 0101 = 21 
 3 + 10 = 1100 + 1010 = (1) 0110 = 22 
 3 + 11 = 1100 + 1011 = (1) 0111 = 23 
 3 + 12 = 1100 + 1100 = (1) 1000 = 24 
 3 + 13 = 1100 + 1101 = (1) 1001 = 25 
 3 + 14 = 1100 + 1110 = (1) 1010 = 26 
 3 + 15 = 1100 + 1111 = (1) 1011 = 27 
 4 +  0 = 1000 + 0000 = (0) 1000 = 8 
 4 +  1 = 1000 + 1000 = (1) 0000 = 16 
 4 +  2 = 1000 + 1000 = (1) 0000 = 16 
 4 +  3 = 1000 + 1100 = (1) 0100 = 20 
 4 +  4 = 1000 + 1000 = (1) 0000 = 16 
 4 +  5 = 1000 + 1010 = (1) 0010 = 18 
 4 +  6 = 1000 + 1100 = (1) 0100 = 20 
 4 +  7 = 1000 + 1110 = (1) 0110 = 22 
 4 +  8 = 1000 + 1000 = (1) 0000 = 16 
 4 +  9 = 1000 + 1001 = (1) 0001 = 17 
 4 + 10 = 1000 + 1010 = (1) 0010 = 18 
 4 + 11 = 1000 + 1011 = (1) 0011 = 19 
 4 + 12 = 1000 + 1100 = (1) 0100 = 20 
 4 + 13 = 1000 + 1101 = (1) 0101 = 21 
 4 + 14 = 1000 + 1110 = (1) 0110 = 22 
 4 + 15 = 1000 + 1111 = (1) 0111 = 23 
 5 +  0 = 1010 + 0000 = (0) 1010 = 10 
 5 +  1 = 1010 + 1000 = (1) 0010 = 18 
 5 +  2 = 1010 + 1000 = (1) 0010 = 18 
 5 +  3 = 1010 + 1100 = (1) 0110 = 22 
 5 +  4 = 1010 + 1000 = (1) 0010 = 18 
 5 +  5 = 1010 + 1010 = (1) 0100 = 20 
 5 +  6 = 1010 + 1100 = (1) 0110 = 22 
 5 +  7 = 1010 + 1110 = (1) 1000 = 24 
 5 +  8 = 1010 + 1000 = (1) 0010 = 18 
 5 +  9 = 1010 + 1001 = (1) 0011 = 19 
 5 + 10 = 1010 + 1010 = (1) 0100 = 20 
 5 + 11 = 1010 + 1011 = (1) 0101 = 21 
 5 + 12 = 1010 + 1100 = (1) 0110 = 22 
 5 + 13 = 1010 + 1101 = (1) 0111 = 23 
 5 + 14 = 1010 + 1110 = (1) 1000 = 24 
 5 + 15 = 1010 + 1111 = (1) 1001 = 25 
 6 +  0 = 1100 + 0000 = (0) 1100 = 12 
 6 +  1 = 1100 + 1000 = (1) 0100 = 20 
 6 +  2 = 1100 + 1000 = (1) 0100 = 20 
 6 +  3 = 1100 + 1100 = (1) 1000 = 24 
 6 +  4 = 1100 + 1000 = (1) 0100 = 20 
 6 +  5 = 1100 + 1010 = (1) 0110 = 22 
 6 +  6 = 1100 + 1100 = (1) 1000 = 24 
 6 +  7 = 1100 + 1110 = (1) 1010 = 26 
 6 +  8 = 1100 + 1000 = (1) 0100 = 20 
 6 +  9 = 1100 + 1001 = (1) 0101 = 21 
 6 + 10 = 1100 + 1010 = (1) 0110 = 22 
 6 + 11 = 1100 + 1011 = (1) 0111 = 23 
 6 + 12 = 1100 + 1100 = (1) 1000 = 24 
 6 + 13 = 1100 + 1101 = (1) 1001 = 25 
 6 + 14 = 1100 + 1110 = (1) 1010 = 26 
 6 + 15 = 1100 + 1111 = (1) 1011 = 27 
 7 +  0 = 1110 + 0000 = (0) 1110 = 14 
 7 +  1 = 1110 + 1000 = (1) 0110 = 22 
 7 +  2 = 1110 + 1000 = (1) 0110 = 22 
 7 +  3 = 1110 + 1100 = (1) 1010 = 26 
 7 +  4 = 1110 + 1000 = (1) 0110 = 22 
 7 +  5 = 1110 + 1010 = (1) 1000 = 24 
 7 +  6 = 1110 + 1100 = (1) 1010 = 26 
 7 +  7 = 1110 + 1110 = (1) 1100 = 28 
 7 +  8 = 1110 + 1000 = (1) 0110 = 22 
 7 +  9 = 1110 + 1001 = (1) 0111 = 23 
 7 + 10 = 1110 + 1010 = (1) 1000 = 24 
 7 + 11 = 1110 + 1011 = (1) 1001 = 25 
 7 + 12 = 1110 + 1100 = (1) 1010 = 26 
 7 + 13 = 1110 + 1101 = (1) 1011 = 27 
 7 + 14 = 1110 + 1110 = (1) 1100 = 28 
 7 + 15 = 1110 + 1111 = (1) 1101 = 29 
 8 +  0 = 1000 + 0000 = (0) 1000 = 8 
 8 +  1 = 1000 + 1000 = (1) 0000 = 16 
 8 +  2 = 1000 + 1000 = (1) 0000 = 16 
 8 +  3 = 1000 + 1100 = (1) 0100 = 20 
 8 +  4 = 1000 + 1000 = (1) 0000 = 16 
 8 +  5 = 1000 + 1010 = (1) 0010 = 18 
 8 +  6 = 1000 + 1100 = (1) 0100 = 20 
 8 +  7 = 1000 + 1110 = (1) 0110 = 22 
 8 +  8 = 1000 + 1000 = (1) 0000 = 16 
 8 +  9 = 1000 + 1001 = (1) 0001 = 17 
 8 + 10 = 1000 + 1010 = (1) 0010 = 18 
 8 + 11 = 1000 + 1011 = (1) 0011 = 19 
 8 + 12 = 1000 + 1100 = (1) 0100 = 20 
 8 + 13 = 1000 + 1101 = (1) 0101 = 21 
 8 + 14 = 1000 + 1110 = (1) 0110 = 22 
 8 + 15 = 1000 + 1111 = (1) 0111 = 23 
 9 +  0 = 1001 + 0000 = (0) 1001 = 9 
 9 +  1 = 1001 + 1000 = (1) 0001 = 17 
 9 +  2 = 1001 + 1000 = (1) 0001 = 17 
 9 +  3 = 1001 + 1100 = (1) 0101 = 21 
 9 +  4 = 1001 + 1000 = (1) 0001 = 17 
 9 +  5 = 1001 + 1010 = (1) 0011 = 19 
 9 +  6 = 1001 + 1100 = (1) 0101 = 21 
 9 +  7 = 1001 + 1110 = (1) 0111 = 23 
 9 +  8 = 1001 + 1000 = (1) 0001 = 17 
 9 +  9 = 1001 + 1001 = (1) 0010 = 18 
 9 + 10 = 1001 + 1010 = (1) 0011 = 19 
 9 + 11 = 1001 + 1011 = (1) 0100 = 20 
 9 + 12 = 1001 + 1100 = (1) 0101 = 21 
 9 + 13 = 1001 + 1101 = (1) 0110 = 22 
 9 + 14 = 1001 + 1110 = (1) 0111 = 23 
 9 + 15 = 1001 + 1111 = (1) 1000 = 24 
10 +  0 = 1010 + 0000 = (0) 1010 = 10 
10 +  1 = 1010 + 1000 = (1) 0010 = 18 
10 +  2 = 1010 + 1000 = (1) 0010 = 18 
10 +  3 = 1010 + 1100 = (1) 0110 = 22 
10 +  4 = 1010 + 1000 = (1) 0010 = 18 
10 +  5 = 1010 + 1010 = (1) 0100 = 20 
10 +  6 = 1010 + 1100 = (1) 0110 = 22 
10 +  7 = 1010 + 1110 = (1) 1000 = 24 
10 +  8 = 1010 + 1000 = (1) 0010 = 18 
10 +  9 = 1010 + 1001 = (1) 0011 = 19 
10 + 10 = 1010 + 1010 = (1) 0100 = 20 
10 + 11 = 1010 + 1011 = (1) 0101 = 21 
10 + 12 = 1010 + 1100 = (1) 0110 = 22 
10 + 13 = 1010 + 1101 = (1) 0111 = 23 
10 + 14 = 1010 + 1110 = (1) 1000 = 24 
10 + 15 = 1010 + 1111 = (1) 1001 = 25 
11 +  0 = 1011 + 0000 = (0) 1011 = 11 
11 +  1 = 1011 + 1000 = (1) 0011 = 19 
11 +  2 = 1011 + 1000 = (1) 0011 = 19 
11 +  3 = 1011 + 1100 = (1) 0111 = 23 
11 +  4 = 1011 + 1000 = (1) 0011 = 19 
11 +  5 = 1011 + 1010 = (1) 0101 = 21 
11 +  6 = 1011 + 1100 = (1) 0111 = 23 
11 +  7 = 1011 + 1110 = (1) 1001 = 25 
11 +  8 = 1011 + 1000 = (1) 0011 = 19 
11 +  9 = 1011 + 1001 = (1) 0100 = 20 
11 + 10 = 1011 + 1010 = (1) 0101 = 21 
11 + 11 = 1011 + 1011 = (1) 0110 = 22 
11 + 12 = 1011 + 1100 = (1) 0111 = 23 
11 + 13 = 1011 + 1101 = (1) 1000 = 24 
11 + 14 = 1011 + 1110 = (1) 1001 = 25 
11 + 15 = 1011 + 1111 = (1) 1010 = 26 
12 +  0 = 1100 + 0000 = (0) 1100 = 12 
12 +  1 = 1100 + 1000 = (1) 0100 = 20 
12 +  2 = 1100 + 1000 = (1) 0100 = 20 
12 +  3 = 1100 + 1100 = (1) 1000 = 24 
12 +  4 = 1100 + 1000 = (1) 0100 = 20 
12 +  5 = 1100 + 1010 = (1) 0110 = 22 
12 +  6 = 1100 + 1100 = (1) 1000 = 24 
12 +  7 = 1100 + 1110 = (1) 1010 = 26 
12 +  8 = 1100 + 1000 = (1) 0100 = 20 
12 +  9 = 1100 + 1001 = (1) 0101 = 21 
12 + 10 = 1100 + 1010 = (1) 0110 = 22 
12 + 11 = 1100 + 1011 = (1) 0111 = 23 
12 + 12 = 1100 + 1100 = (1) 1000 = 24 
12 + 13 = 1100 + 1101 = (1) 1001 = 25 
12 + 14 = 1100 + 1110 = (1) 1010 = 26 
12 + 15 = 1100 + 1111 = (1) 1011 = 27 
13 +  0 = 1101 + 0000 = (0) 1101 = 13 
13 +  1 = 1101 + 1000 = (1) 0101 = 21 
13 +  2 = 1101 + 1000 = (1) 0101 = 21 
13 +  3 = 1101 + 1100 = (1) 1001 = 25 
13 +  4 = 1101 + 1000 = (1) 0101 = 21 
13 +  5 = 1101 + 1010 = (1) 0111 = 23 
13 +  6 = 1101 + 1100 = (1) 1001 = 25 
13 +  7 = 1101 + 1110 = (1) 1011 = 27 
13 +  8 = 1101 + 1000 = (1) 0101 = 21 
13 +  9 = 1101 + 1001 = (1) 0110 = 22 
13 + 10 = 1101 + 1010 = (1) 0111 = 23 
13 + 11 = 1101 + 1011 = (1) 1000 = 24 
13 + 12 = 1101 + 1100 = (1) 1001 = 25 
13 + 13 = 1101 + 1101 = (1) 1010 = 26 
13 + 14 = 1101 + 1110 = (1) 1011 = 27 
13 + 15 = 1101 + 1111 = (1) 1100 = 28 
14 +  0 = 1110 + 0000 = (0) 1110 = 14 
14 +  1 = 1110 + 1000 = (1) 0110 = 22 
14 +  2 = 1110 + 1000 = (1) 0110 = 22 
14 +  3 = 1110 + 1100 = (1) 1010 = 26 
14 +  4 = 1110 + 1000 = (1) 0110 = 22 
14 +  5 = 1110 + 1010 = (1) 1000 = 24 
14 +  6 = 1110 + 1100 = (1) 1010 = 26 
14 +  7 = 1110 + 1110 = (1) 1100 = 28 
14 +  8 = 1110 + 1000 = (1) 0110 = 22 
14 +  9 = 1110 + 1001 = (1) 0111 = 23 
14 + 10 = 1110 + 1010 = (1) 1000 = 24 
14 + 11 = 1110 + 1011 = (1) 1001 = 25 
14 + 12 = 1110 + 1100 = (1) 1010 = 26 
14 + 13 = 1110 + 1101 = (1) 1011 = 27 
14 + 14 = 1110 + 1110 = (1) 1100 = 28 
14 + 15 = 1110 + 1111 = (1) 1101 = 29 
15 +  0 = 1111 + 0000 = (0) 1111 = 15 
15 +  1 = 1111 + 1000 = (1) 0111 = 23 
15 +  2 = 1111 + 1000 = (1) 0111 = 23 
15 +  3 = 1111 + 1100 = (1) 1011 = 27 
15 +  4 = 1111 + 1000 = (1) 0111 = 23 
15 +  5 = 1111 + 1010 = (1) 1001 = 25 
15 +  6 = 1111 + 1100 = (1) 1011 = 27 
15 +  7 = 1111 + 1110 = (1) 1101 = 29 
15 +  8 = 1111 + 1000 = (1) 0111 = 23 
15 +  9 = 1111 + 1001 = (1) 1000 = 24 
15 + 10 = 1111 + 1010 = (1) 1001 = 25 
15 + 11 = 1111 + 1011 = (1) 1010 = 26 
15 + 12 = 1111 + 1100 = (1) 1011 = 27 
15 + 13 = 1111 + 1101 = (1) 1100 = 28 
15 + 14 = 1111 + 1110 = (1) 1101 = 29 
15 + 15 = 1111 + 1111 = (1) 1110 = 30

AutoHotkey

Works with: AutoHotkey 1.1
A := 13
B := 9
N := FourBitAdd(A, B)
MsgBox, % A " + " B ":`n"
	. GetBin4(A) " + " GetBin4(B) " = " N.S " (Carry = " N.C ")"
return

Xor(A, B) {
	return (~A & B) | (A & ~B)
}

HalfAdd(A, B) {
	return {"S": Xor(A, B), "C": A & B}
}

FullAdd(A, B, C=0) {
	X := HalfAdd(A, C)
	Y := HalfAdd(B, X.S)
	return {"S": Y.S, "C": X.C | Y.C}
}

FourBitAdd(A, B, C=0) {
	A := GetFourBits(A)
	B := GetFourBits(B)
	X := FullAdd(A[4], B[4], C)
	Y := FullAdd(A[3], B[3], X.C)
	W := FullAdd(A[2], B[2], Y.C)
	Z := FullAdd(A[1], B[1], W.C)
	return {"S": Z.S W.S Y.S X.S, "C": Z.C}
}

GetFourBits(N) {
	if (N < 0 || N > 15)
		return -1
	return StrSplit(GetBin4(N))
}

GetBin4(N) {
	Loop 4
		Res := Mod(N, 2) Res, N := N >> 1
	return, Res
}
Output:
13 + 9:
1101 + 1001 = 0110 (Carry = 1)

AutoIt

Functions

Func _NOT($_A)
	Return (Not $_A) *1
EndFunc  ;==>_NOT

Func _AND($_A, $_B)
	Return BitAND($_A, $_B)
EndFunc  ;==>_AND

Func _OR($_A, $_B)
	Return BitOR($_A, $_B)
EndFunc  ;==>_OR

Func _XOR($_A, $_B)
	Return _OR( _
		_AND( $_A, _NOT($_B) ), _
		_AND( _NOT($_A), $_B) )
EndFunc  ;==>_XOR

Func _HalfAdder($_A, $_B, ByRef $_CO)
	$_CO = _AND($_A, $_B)
	Return _XOR($_A, $_B)
EndFunc  ;==>_HalfAdder

Func _FullAdder($_A, $_B, $_CI, ByRef $_CO)
	Local $CO1, $CO2, $Q1, $Q2
	$Q1 = _HalfAdder($_A, $_B, $CO1)
	$Q2 = _HalfAdder($Q1, $_CI, $CO2)
	$_CO = _OR($CO2, $CO1)
	Return $Q2
EndFunc  ;==>_FullAdder

Func _4BitAdder($_A1, $_A2, $_A3, $_A4, $_B1, $_B2, $_B3, $_B4, $_CI, ByRef $_CO)
	Local $CO1, $CO2, $CO3, $CO4, $Q1, $Q2, $Q3, $Q4
	$Q1 = _FullAdder($_A4, $_B4, $_CI, $CO1)
	$Q2 = _FullAdder($_A3, $_B3, $CO1, $CO2)
	$Q3 = _FullAdder($_A2, $_B2, $CO2, $CO3)
	$Q4 = _FullAdder($_A1, $_B1, $CO3, $CO4)
	$_CO = $CO4
	Return $Q4 & $Q3 & $Q2 & $Q1
EndFunc  ;==>_4BitAdder

Example

Local $CarryOut, $sResult
$sResult = _4BitAdder(0, 0, 1, 1, 0, 1, 1, 1, 0, $CarryOut)  ; adds 3 + 7
ConsoleWrite('result: ' & $sResult & '  ==> carry out: ' & $CarryOut & @LF)

$sResult = _4BitAdder(1, 0, 1, 1, 1, 0, 0, 0, 0, $CarryOut)  ; adds 11 + 8
ConsoleWrite('result: ' & $sResult & '  ==> carry out: ' & $CarryOut & @LF)
Output:
result: 1010  ==> carry out: 0
result: 0011  ==> carry out: 1

--BugFix (talk) 17:10, 14 November 2013 (UTC)

BASIC

Applesoft BASIC

100 S$ = "1100 + 1100 = " : GOSUB 400
110 S$ = "1100 + 1101 = " : GOSUB 400
120 S$ = "1100 + 1110 = " : GOSUB 400
130 S$ = "1100 + 1111 = " : GOSUB 400
140 S$ = "1101 + 0000 = " : GOSUB 400
150 S$ = "1101 + 0001 = " : GOSUB 400
160 S$ = "1101 + 0010 = " : GOSUB 400
170 S$ = "1101 + 0011 = " : GOSUB 400
180 END

400 A0 = VAL(MID$(S$, 4, 1))
410 A1 = VAL(MID$(S$, 3, 1))
420 A2 = VAL(MID$(S$, 2, 1))
430 A3 = VAL(MID$(S$, 1, 1))
440 B0 = VAL(MID$(S$, 11, 1))
450 B1 = VAL(MID$(S$, 10, 1))
460 B2 = VAL(MID$(S$, 9, 1))
470 B3 = VAL(MID$(S$, 8, 1))
480 GOSUB 600
490 PRINT S$;

REM 4 BIT PRINT
500 PRINT C;S3;S2;S1;S0
510 RETURN

REM 4 BIT ADD
REM  ADD A3 A2 A1 A0 TO B3 B2 B1 B0
REM  RESULT IN S3 S2 S1 S0
REM  CARRY IN C
600 C = 0
610 A = A0 : B = B0 : GOSUB 700 : S0 = S
620 A = A1 : B = B1 : GOSUB 700 : S1 = S
630 A = A2 : B = B2 : GOSUB 700 : S2 = S
640 A = A3 : B = B3 : GOSUB 700 : S3 = S
650 RETURN

REM FULL ADDER
REM  ADD A + B + C
REM  RESULT IN S
REM  CARRY IN C
700 BH = B : B = C : GOSUB 800 : C1 = C
710 A = S : B = BH : GOSUB 800 : C2 = C
720 C = C1 OR C2
730 RETURN

REM HALF ADDER
REM  ADD A + B
REM  RESULT IN S
REM  CARRY IN C
800 GOSUB 900 : S = C
810 C = A AND B
820 RETURN

REM XOR GATE
REM  A XOR B
REM  RESULT IN C
900 C = A AND NOT B
910 D = B AND NOT A
920 C = C OR D
930 RETURN

BBC BASIC

      @% = 2
      PRINT "1100 + 1100 = ";
      PROC4bitadd(1,1,0,0, 1,1,0,0, e,d,c,b,a) : PRINT e,d,c,b,a
      PRINT "1100 + 1101 = ";
      PROC4bitadd(1,1,0,0, 1,1,0,1, e,d,c,b,a) : PRINT e,d,c,b,a
      PRINT "1100 + 1110 = ";
      PROC4bitadd(1,1,0,0, 1,1,1,0, e,d,c,b,a) : PRINT e,d,c,b,a
      PRINT "1100 + 1111 = ";
      PROC4bitadd(1,1,0,0, 1,1,1,1, e,d,c,b,a) : PRINT e,d,c,b,a
      PRINT "1101 + 0000 = ";
      PROC4bitadd(1,1,0,1, 0,0,0,0, e,d,c,b,a) : PRINT e,d,c,b,a
      PRINT "1101 + 0001 = ";
      PROC4bitadd(1,1,0,1, 0,0,0,1, e,d,c,b,a) : PRINT e,d,c,b,a
      PRINT "1101 + 0010 = ";
      PROC4bitadd(1,1,0,1, 0,0,1,0, e,d,c,b,a) : PRINT e,d,c,b,a
      PRINT "1101 + 0011 = ";
      PROC4bitadd(1,1,0,1, 0,0,1,1, e,d,c,b,a) : PRINT e,d,c,b,a
      END
      
      DEF PROC4bitadd(a3&, a2&, a1&, a0&, b3&, b2&, b1&, b0&, \
      \   RETURN c3&, RETURN s3&, RETURN s2&, RETURN s1&, RETURN s0&)
      LOCAL c0&, c1&, c2&
      PROCfulladder(a0&, b0&,   0, s0&, c0&)
      PROCfulladder(a1&, b1&, c0&, s1&, c1&)
      PROCfulladder(a2&, b2&, c1&, s2&, c2&)
      PROCfulladder(a3&, b3&, c2&, s3&, c3&)
      ENDPROC
      
      DEF PROCfulladder(a&, b&, c&, RETURN s&, RETURN c1&)
      LOCAL x&, y&, z&
      PROChalfadder(a&, c&, x&, y&)
      PROChalfadder(x&, b&, s&, z&)
      c1& = y& OR z&
      ENDPROC
      
      DEF PROChalfadder(a&, b&, RETURN s&, RETURN c&)
      s& = FNxorgate(a&, b&)
      c& = a& AND b&
      ENDPROC
      
      DEF FNxorgate(a&, b&)
      LOCAL c&, d&
      c& = a& AND NOT b&
      d& = b& AND NOT a&
      = c& OR d&
Output:
1100 + 1100 =  1 1 0 0 0
1100 + 1101 =  1 1 0 0 1
1100 + 1110 =  1 1 0 1 0
1100 + 1111 =  1 1 0 1 1
1101 + 0000 =  0 1 1 0 1
1101 + 0001 =  0 1 1 1 0
1101 + 0010 =  0 1 1 1 1
1101 + 0011 =  1 0 0 0 0

Batch File

@echo off
setlocal enabledelayedexpansion

:: ":main" is where all the non-logic-gate stuff happens
:main
:: User input two 4-digit binary numbers
:: There is no error checking for these numbers, however if the first 4 digits of both inputs are in binary...
:: The program will use them. All non-binary numbers are treated as 0s, but having less than 4 digits will crash it
set /p "input1=First 4-Bit Binary Number: "
set /p "input2=Second 4-Bit Binary Number: "

:: Put the first 4 digits of the binary numbers and separate them into "A[]" for input A and "B[]" for input B
for /l %%i in (0,1,3) do (
  set A%%i=!input1:~%%i,1!
  set B%%i=!input2:~%%i,1!
)

:: Run the 4-bit Adder with "A[]" and "B[]" as parameters. The program supports a 9th parameter for a Carry input
call:_4bitAdder %A3% %A2% %A1% %A0% %B3% %B2% %B1% %B0% 0

:: Display the answer and exit
echo %input1% + %input2% = %outputC%%outputS4%%outputS3%%outputS2%%outputS1%
pause>nul
exit /b

:: Function for the 4-bit Adder following the logic given
:_4bitAdder
set inputA1=%1
set inputA2=%2
set inputA3=%3
set inputA4=%4

set inputB1=%5
set inputB2=%6
set inputB3=%7
set inputB4=%8

set inputC=%9

call:_FullAdder %inputA1% %inputB1% %inputC%
set outputS1=%outputS%
set inputC=%outputC%

call:_FullAdder %inputA2% %inputB2% %inputC%
set outputS2=%outputS%
set inputC=%outputC%

call:_FullAdder %inputA3% %inputB3% %inputC%
set outputS3=%outputS%
set inputC=%outputC%

call:_FullAdder %inputA4% %inputB4% %inputC%
set outputS4=%outputS%
set inputC=%outputC%

:: In order return more than one number (of which is usually done via 'exit /b') we declare them while ending the local environment
endlocal && set "outputS1=%outputS1%" && set "outputS2=%outputS2%" && set "outputS3=%outputS3%" && set "outputS4=%outputS4%" && set "outputC=%inputC%"
exit /b

:: Function for the 1-bit Adder following the logic given
:_FullAdder
setlocal
set inputA=%1
set inputB=%2
set inputC1=%3

call:_halfAdder %inputA% %inputB%
set inputA1=%outputS%
set inputA2=%inputA1%
set inputC2=%outputC%

call:_HalfAdder %inputA1% %inputC1%
set outputS=%outputS%
set inputC1=%outputC%

call:_Or %inputC1% %inputC2%
set outputC=%errorlevel%

endlocal && set "outputS=%outputS%" && set "outputC=%outputC%"
exit /b

:: Function for the half-bit adder following the logic given
:_halfAdder
setlocal
set inputA1=%1
set inputA2=%inputA1%
set inputB1=%2
set inputB2=%inputB1%

call:_XOr %inputA1% %inputB2%
set outputS=%errorlevel%

call:_And %inputA2% %inputB2%
set outputC=%errorlevel%

endlocal && set "outputS=%outputS%" && set "outputC=%outputC%"
exit /b

:: Function for the XOR-gate following the logic given
:_XOr
setlocal
set inputA1=%1
set inputB1=%2

call:_Not %inputA1%
set inputA2=%errorlevel%

call:_Not %inputB1%
set inputB2=%errorlevel%

call:_And %inputA1% %inputB2%
set inputA=%errorlevel%

call:_And %inputA2% %inputB1%
set inputB=%errorlevel%

call:_Or %inputA% %inputB%
set outputA=%errorlevel%

:: As there is only one output, we can use 'exit /b {errorlevel}' to return a specified errorlevel
exit /b %outputA%

:: The basic 3 logic gates that every other funtion is composed of
:_Not
setlocal
if %1==0 exit /b 1
exit /b 0
:_Or
setlocal
if %1==1 exit /b 1
if %2==1 exit /b 1
exit /b 0
:_And
setlocal
if %1==1 if %2==1 exit /b 1
exit /b 0
Output:
First 4-Bit Binary Number: 1011
Second 4-Bit Binary Number: 0111
1011 + 0111 = 10010

C

#include <stdio.h>

typedef char pin_t;
#define IN const pin_t *
#define OUT pin_t *
#define PIN(X) pin_t _##X; pin_t *X = & _##X;
#define V(X) (*(X))

/* a NOT that does not soil the rest of the host of the single bit */
#define NOT(X) (~(X)&1)

/* a shortcut to "implement" a XOR using only NOT, AND and OR gates, as
   task requirements constrain */
#define XOR(X,Y) ((NOT(X)&(Y)) | ((X)&NOT(Y)))

void halfadder(IN a, IN b, OUT s, OUT c)
{
  V(s) = XOR(V(a), V(b));
  V(c) = V(a) & V(b);
}

void fulladder(IN a, IN b, IN ic, OUT s, OUT oc)
{
  PIN(ps); PIN(pc); PIN(tc);

  halfadder(/*INPUT*/a, b, /*OUTPUT*/ps, pc);
  halfadder(/*INPUT*/ps, ic, /*OUTPUT*/s, tc);
  V(oc) = V(tc) | V(pc);
}

void fourbitsadder(IN a0, IN a1, IN a2, IN a3,
		   IN b0, IN b1, IN b2, IN b3,
		   OUT o0, OUT o1, OUT o2, OUT o3,
		   OUT overflow)
{
  PIN(zero); V(zero) = 0;
  PIN(tc0); PIN(tc1); PIN(tc2);

  fulladder(/*INPUT*/a0, b0, zero, /*OUTPUT*/o0, tc0);
  fulladder(/*INPUT*/a1, b1, tc0,  /*OUTPUT*/o1, tc1);
  fulladder(/*INPUT*/a2, b2, tc1,  /*OUTPUT*/o2, tc2);
  fulladder(/*INPUT*/a3, b3, tc2,  /*OUTPUT*/o3, overflow);
}


int main()
{
  PIN(a0); PIN(a1); PIN(a2); PIN(a3);
  PIN(b0); PIN(b1); PIN(b2); PIN(b3);
  PIN(s0); PIN(s1); PIN(s2); PIN(s3);
  PIN(overflow);

  V(a3) = 0; V(b3) = 1;
  V(a2) = 0; V(b2) = 1;
  V(a1) = 1; V(b1) = 1;
  V(a0) = 0; V(b0) = 0;

  fourbitsadder(a0, a1, a2, a3, /* INPUT */
		b0, b1, b2, b3,
		s0, s1, s2, s3, /* OUTPUT */
		overflow);

  printf("%d%d%d%d + %d%d%d%d = %d%d%d%d, overflow = %d\n",
	 V(a3), V(a2), V(a1), V(a0),
	 V(b3), V(b2), V(b1), V(b0),
	 V(s3), V(s2), V(s1), V(s0),
	 V(overflow));
  
  return 0;
}

C#

Works with: C# version 3+
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace RosettaCodeTasks.FourBitAdder
{
	public struct BitAdderOutput
	{
		public bool S { get; set; }
		public bool C { get; set; }
		public override string ToString ( )
		{
			return "S" + ( S ? "1" : "0" ) + "C" + ( C ? "1" : "0" );
		}
	}
	public struct Nibble
	{
		public bool _1 { get; set; }
		public bool _2 { get; set; }
		public bool _3 { get; set; }
		public bool _4 { get; set; }
		public override string ToString ( )
		{
			return ( _4 ? "1" : "0" )
				+ ( _3 ? "1" : "0" )
				+ ( _2 ? "1" : "0" )
				+ ( _1 ? "1" : "0" );
		}
	}
	public struct FourBitAdderOutput
	{
		public Nibble N { get; set; }
		public bool C { get; set; }
		public override string ToString ( )
		{
			return N.ToString ( ) + "c" + ( C ? "1" : "0" );
		}
	}

	public static class LogicGates
	{
		// Basic Gates
		public static bool Not ( bool A ) { return !A; }
		public static bool And ( bool A, bool B ) { return A && B; }
		public static bool Or ( bool A, bool B ) { return A || B; }

		// Composite Gates
		public static bool Xor ( bool A, bool B ) {	return Or ( And ( A, Not ( B ) ), ( And ( Not ( A ), B ) ) ); }
	}

	public static class ConstructiveBlocks
	{
		public static BitAdderOutput HalfAdder ( bool A, bool B )
		{
			return new BitAdderOutput ( ) { S = LogicGates.Xor ( A, B ), C = LogicGates.And ( A, B ) };
		}

		public static BitAdderOutput FullAdder ( bool A, bool B, bool CI )
		{
			BitAdderOutput HA1 = HalfAdder ( CI, A );
			BitAdderOutput HA2 = HalfAdder ( HA1.S, B );

			return new BitAdderOutput ( ) { S = HA2.S, C = LogicGates.Or ( HA1.C, HA2.C ) };
		}

		public static FourBitAdderOutput FourBitAdder ( Nibble A, Nibble B, bool CI )
		{

			BitAdderOutput FA1 = FullAdder ( A._1, B._1, CI );
			BitAdderOutput FA2 = FullAdder ( A._2, B._2, FA1.C );
			BitAdderOutput FA3 = FullAdder ( A._3, B._3, FA2.C );
			BitAdderOutput FA4 = FullAdder ( A._4, B._4, FA3.C );

			return new FourBitAdderOutput ( ) { N = new Nibble ( ) { _1 = FA1.S, _2 = FA2.S, _3 = FA3.S, _4 = FA4.S }, C = FA4.C };
		}

		public static void Test ( )
		{
			Console.WriteLine ( "Four Bit Adder" );

			for ( int i = 0; i < 256; i++ )
			{
				Nibble A = new Nibble ( ) { _1 = false, _2 = false, _3 = false, _4 = false };
				Nibble B = new Nibble ( ) { _1 = false, _2 = false, _3 = false, _4 = false };
				if ( (i & 1) == 1)
				{
					A._1 = true;
				}
				if ( ( i & 2 ) == 2 )
				{
					A._2 = true;
				}
				if ( ( i & 4 ) == 4 )
				{
					A._3 = true;
				}
				if ( ( i & 8 ) == 8 )
				{
					A._4 = true;
				}
				if ( ( i & 16 ) == 16 )
				{
					B._1 = true;
				}
				if ( ( i & 32 ) == 32)
				{
					B._2 = true;
				}
				if ( ( i & 64 ) == 64 )
				{
					B._3 = true;
				}
				if ( ( i & 128 ) == 128 )
				{
					B._4 = true;
				}

				Console.WriteLine ( "{0} + {1} = {2}", A.ToString ( ), B.ToString ( ), FourBitAdder( A, B, false ).ToString ( ) );

			}

			Console.WriteLine ( );
		}

	}
}

C++

See Four bit adder/C++

Clojure

(ns rosettacode.adder
  (:use clojure.test))

(defn xor-gate [a b]
  (or (and a (not b)) (and b (not a))))

(defn half-adder [a b]
  "output: (S C)"
  (cons (xor-gate a b) (list (and a b))))

(defn full-adder [a b c]
  "output: (C S)"
  (let [HA-ca (half-adder c a)
        HA-ca->sb (half-adder (first HA-ca) b)]
    (cons (or (second HA-ca) (second HA-ca->sb))
          (list (first HA-ca->sb)))))

(defn n-bit-adder
  "first bits on the list are low order bits
1 = true
2 = false true
3 = true true
4 = false false true..."
  can add numbers of different bit-length
  ([a-bits b-bits] (n-bit-adder a-bits b-bits false))
  ([a-bits b-bits carry]
  (let [added (full-adder (first a-bits) (first b-bits) carry)]
    (if(and (nil? a-bits) (nil? b-bits))
      (if carry (list carry) '())
      (cons (second added) (n-bit-adder (next a-bits) (next b-bits) (first added)))))))

;use:
(n-bit-adder [true true true true true true] [true true true true true true])
=> (false true true true true true true)

Second Clojure solution

(ns rosetta.fourbit)

;; a bit is represented as a boolean (true/false)
;; a word is a big-endian vector of bits [true false true true] = 11
;; multiple values are returned as vectors

(defn or-gate [a b]
  (or a b))

(defn and-gate [a b]
  (and a b))

(defn not-gate [a]
  (not a))

(defn xor-gate [a b]
  (or-gate (and-gate (not-gate a) b) (and-gate a (not-gate b))))

(defn half-adder [a b]
  "result is [carry sum]"
  (let [carry (and-gate a b)
        sum (xor-gate a b)]
    [carry sum]))

(defn full-adder [a b c0]
  "result is [carry sum]"
  (let [[ca sa] (half-adder c0 a)
        [cb sb] (half-adder sa b)]
    [(or-gate ca cb) sb]))

(defn nbit-adder [va vb]
  "va and vb should be big endian bit vectors of the same size. The result
is a bit vector having one more bit (carry) than args."
  {:pre [(= (count va) (count vb))]}
  (let [[c sums] (reduce (fn [[carry sums] [a b]]
                              (let [[c s] (full-adder a b carry)]
                                [c (conj sums s)]))
                         ;; initial value: false carry and an empty list of sums
                         [false ()]
                         ;; rseq is constant-time reverse for vectors
                         (map vector (rseq va) (rseq vb)))]
    (vec (conj sums c))))

(defn four-bit-adder [a4 a3 a2 a1 b4 b3 b2 b1]
  "Returns [carry s4 s3 s2 s1]"
  (nbit-adder [a4 a3 a2 a1] [b4 b3 b2 b1]))

(comment
(four-bit-adder false true true false  true false true true)
;; [true false false false true]
)

Using Bitwise Operators

(defn to-binary-seq [^long x]
  (map #(- (int %) (int \0))
       (Long/toBinaryString x)))

(defn half-adder [a b]
  [(bit-xor a b)
   (bit-and a b)])

(defn full-adder [a b carry]
  (let [added (half-adder b carry)
        half-sum (first added)]
    [(first (half-adder a half-sum))
     (bit-or (second (half-adder a half-sum)) (second added))]))

(defn ripple-carry-adder [a b]
  (loop [a (reverse a)
         b (reverse b)
         sum '()
         carry 0]
    (let [added (full-adder (first a) (first b) carry)]
      (if (and (empty? (next a)) (empty? (next b)))
        (conj sum (first added) (bit-or carry 1))
        (recur (next a) (next b) (conj sum (first added)) (second added))))))

(deftest adder
  (is (= (Long/parseLong (apply str (ripple-carry-adder (to-binary-seq 10) (to-binary-seq 10))) 2)
         (+ 10 10)))
  (is (= (Long/parseLong (apply str (ripple-carry-adder (to-binary-seq 50) (to-binary-seq 50))) 2)
         (+ 50 50)))
  (is (= (Long/parseLong (apply str (ripple-carry-adder (to-binary-seq 32) (to-binary-seq 38))) 2)
         (+ 32 38)))
  (is (= (Long/parseLong (apply str (ripple-carry-adder (to-binary-seq 130) (to-binary-seq 250))) 2)
         (+ 130 250))))

COBOL

       program-id. test-add.
       environment division.
       configuration section.
       special-names.
           class bin is "0" "1".
       data division.
       working-storage section.
       1 parms.
        2 a-in pic 9999.
        2 b-in pic 9999.
        2 r-out pic 9999.
        2 c-out pic 9.
       procedure division.
           display "Enter 'A' value (4-bits binary): "
               with no advancing
           accept a-in
           if a-in (1:) not bin
               display "A is not binary"
               stop run
           end-if
           display "Enter 'B' value (4-bits binary): "
               with no advancing
           accept b-in
           if b-in (1:) not bin
               display "B is not binary"
               stop run
           end-if
           call "add-4b" using parms
           display "Carry " c-out " result " r-out
           stop run
           .
       end program test-add.

       program-id. add-4b.
       data division.
       working-storage section.
       1 wk binary.
        2 i pic 9(4).
        2 occurs 5.
         3 a-reg pic 9.
         3 b-reg pic 9.
         3 c-reg pic 9.
         3 r-reg pic 9.
        2 a pic 9.
        2 b pic 9.
        2 c pic 9.
        2 a-not pic 9.
        2 b-not pic 9.
        2 c-not pic 9.
        2 ha-1s pic 9.
        2 ha-1c pic 9.
        2 ha-1s-not pic 9.
        2 ha-1c-not pic 9.
        2 ha-2s pic 9.
        2 ha-2c pic 9.
        2 fa-s pic 9.
        2 fa-c pic 9.
       linkage section.
       1 parms.
        2 a-in pic 9999.
        2 b-in pic 9999.
        2 r-out pic 9999.
        2 c-out pic 9.
       procedure division using parms.
           initialize wk
           perform varying i from 1 by 1
           until i > 4
               move a-in (5 - i:1) to a-reg (i)
               move b-in (5 - i:1) to b-reg (i)
           end-perform
           perform simulate-adder varying i from 1 by 1
               until i > 4
           move c-reg (5) to c-out
           perform varying i from 1 by 1
           until i > 4
               move r-reg (i) to r-out (5 - i:1)
           end-perform
           exit program
           .

       simulate-adder section.
           move a-reg (i) to a
           move b-reg (i) to b
           move c-reg (i) to c
           add a -1 giving a-not
           add b -1 giving b-not
           add c -1 giving c-not

           compute ha-1s = function max (
               function min ( a b-not )
               function min ( b a-not ) )
           compute ha-1c = function min ( a b )
           add ha-1s -1 giving ha-1s-not
           add ha-1c -1 giving ha-1c-not

           compute ha-2s = function max (
               function min ( c ha-1s-not )
               function min ( ha-1s c-not ) )
           compute ha-2c = function min ( c ha-1c )

           compute fa-s = ha-2s
           compute fa-c = function max ( ha-1c ha-2c )

           move fa-s to r-reg (i)
           move fa-c to c-reg (i + 1)
           .
       end program add-4b.
Output:
Enter 'A' value (4-bits binary): 0011
Enter 'B' value (4-bits binary): 1010
Carry 0 result 1101

Enter 'A' value (4-bits binary): 1100
Enter 'B' value (4-bits binary): 1010
Carry 1 result 0110

CoffeeScript

This code models gates as functions. The connection of gates is done via custom logic, which doesn't involve any cheating, but a really good solution would be more constructive, i.e. it would show more of a notion of "connecting" up gates, using some kind of graph data structure.

# ATOMIC GATES
not_gate = (bit) ->
  [1, 0][bit]
  
and_gate = (bit1, bit2) ->
  bit1 and bit2
  
or_gate = (bit1, bit2) ->
  bit1 or bit2
  
# COMPOSED GATES
xor_gate = (A, B) ->
  X = and_gate A, not_gate(B)
  Y = and_gate not_gate(A), B
  or_gate X, Y
  
half_adder = (A, B) ->
  S = xor_gate A, B
  C = and_gate A, B
  [S, C]
  
full_adder = (C0, A, B) ->
  [SA, CA] = half_adder C0, A
  [SB, CB] = half_adder SA, B
  S = SB
  C = or_gate CA, CB
  [S, C]
  
n_bit_adder = (n) ->
  (A_bits, B_bits) ->
    s = []
    C = 0
    for i in [0...n]
      [S, C] = full_adder C, A_bits[i], B_bits[i]
      s.push S
    [s, C]

adder = n_bit_adder(4)  
console.log adder [1, 0, 1, 0], [0, 1, 1, 0]

Common Lisp

;; returns a list of bits: '(sum carry)
(defun half-adder (a b)
  (list (logxor a b) (logand a b)))

;; returns a list of bits: '(sum, carry)
(defun full-adder (a b c-in)
  (let*
    ((h1 (half-adder c-in a))
    (h2 (half-adder (first h1) b)))
    (list (first h2) (logior (second h1) (second h2)))))

;; a and b are lists of 4 bits each
(defun 4-bit-adder (a b)
  (let*
    ((add-1 (full-adder (fourth a) (fourth b) 0))
      (add-2 (full-adder (third a) (third b) (second add-1)))
      (add-3 (full-adder (second a) (second b) (second add-2)))
      (add-4 (full-adder (first a) (first b) (second add-3))))
    (list
      (list (first add-4) (first add-3) (first add-2) (first add-1))
      (second add-4))))

(defun main ()
  (print (4-bit-adder (list 0 0 0 0) (list 0 0 0 0)))   ;; '(0 0 0 0) and 0
  (print (4-bit-adder (list 0 0 0 0) (list 1 1 1 1)))   ;; '(1 1 1 1) and 0
  (print (4-bit-adder (list 1 1 1 1) (list 0 0 0 0)))   ;; '(1 1 1 1) and 0
  (print (4-bit-adder (list 0 1 0 1) (list 1 1 0 0)))   ;; '(0 0 0 1) and 1
  (print (4-bit-adder (list 1 1 1 1) (list 1 1 1 1)))   ;; '(1 1 1 0) and 1
  (print (4-bit-adder (list 1 0 1 0) (list 0 1 0 1)))   ;; '(1 1 1 1) and 0
 )

(main)

output:

((0 0 0 0) 0)
((1 1 1 1) 0)
((1 1 1 1) 0)
((0 0 0 1) 1)
((1 1 1 0) 1)
((1 1 1 1) 0)

D

From the C version. An example of SWAR (SIMD Within A Register) code, that performs 32 (or 64) 4-bit adds in parallel.

import std.stdio, std.traits;

void fourBitsAdder(T)(in T a0, in T a1, in T a2, in T a3,
                      in T b0, in T b1, in T b2, in T b3,
                      out T o0, out T o1,
                      out T o2, out T o3,
                      out T overflow) pure nothrow @nogc {

    // A XOR using only NOT, AND and OR, as task requires.
    static T xor(in T x, in T y) pure nothrow @nogc {
        return (~x & y) | (x & ~y);
    }

    static void halfAdder(in T a, in T b,
                          out T s, out T c) pure nothrow @nogc {
        s = xor(a, b);
        // s = a ^ b; // The built-in D xor.
        c = a & b;
    }

    static void fullAdder(in T a, in T b, in T ic,
                          out T s, out T oc) pure nothrow @nogc {
        T ps, pc, tc;

        halfAdder(/*in*/a, b,   /*out*/ps, pc);
        halfAdder(/*in*/ps, ic, /*out*/s, tc);
        oc = tc | pc;
    }

    T zero, tc0, tc1, tc2;

    fullAdder(/*in*/a0, b0, zero, /*out*/o0, tc0);
    fullAdder(/*in*/a1, b1, tc0,  /*out*/o1, tc1);
    fullAdder(/*in*/a2, b2, tc1,  /*out*/o2, tc2);
    fullAdder(/*in*/a3, b3, tc2,  /*out*/o3, overflow);
}

void main() {
    alias T = size_t;
    static assert(isUnsigned!T);

    enum T one = T.max,
           zero = T.min,
           a0 = zero, a1 = one, a2 = zero, a3 = zero,
           b0 = zero, b1 = one, b2 = one,  b3 = one;
    T s0, s1, s2, s3, overflow;

    fourBitsAdder(/*in*/ a0, a1, a2, a3,
                  /*in*/ b0, b1, b2, b3,
                  /*out*/s0, s1, s2, s3, overflow);

    writefln("      a3 %032b", a3);
    writefln("      a2 %032b", a2);
    writefln("      a1 %032b", a1);
    writefln("      a0 %032b", a0);
    writefln("      +");
    writefln("      b3 %032b", b3);
    writefln("      b2 %032b", b2);
    writefln("      b1 %032b", b1);
    writefln("      b0 %032b", b0);
    writefln("      =");
    writefln("      s3 %032b", s3);
    writefln("      s2 %032b", s2);
    writefln("      s1 %032b", s1);
    writefln("      s0 %032b", s0);
    writefln("overflow %032b", overflow);
}
Output:
      a3 00000000000000000000000000000000
      a2 00000000000000000000000000000000
      a1 11111111111111111111111111111111
      a0 00000000000000000000000000000000
      +
      b3 11111111111111111111111111111111
      b2 11111111111111111111111111111111
      b1 11111111111111111111111111111111
      b0 00000000000000000000000000000000
      =
      s3 00000000000000000000000000000000
      s2 00000000000000000000000000000000
      s1 00000000000000000000000000000000
      s0 00000000000000000000000000000000
overflow 11111111111111111111111111111111

128 4-bit adds in parallel:

import std.stdio, std.traits, core.simd;

void fourBitsAdder(T)(in T a0, in T a1, in T a2, in T a3,
                      in T b0, in T b1, in T b2, in T b3,
                      out T o0, out T o1,
                      out T o2, out T o3,
                      out T overflow) pure nothrow {

    // A XOR using only NOT, AND and OR, as task requires.
    static T xor(in T x, in T y) pure nothrow {
        return (~x & y) | (x & ~y);
    }

    static void halfAdder(in T a, in T b,
                          out T s, out T c) pure nothrow {
        s = xor(a, b);
        // s = a ^ b; // The built-in D xor.
        c = a & b;
    }

    static void fullAdder(in T a, in T b, in T ic,
                          out T s, out T oc) pure nothrow {
        T ps, pc, tc;

        halfAdder(/*in*/a, b,   /*out*/ps, pc);
        halfAdder(/*in*/ps, ic, /*out*/s, tc);
        oc = tc | pc;
    }

    T zero, tc0, tc1, tc2;

    fullAdder(/*in*/a0, b0, zero, /*out*/o0, tc0);
    fullAdder(/*in*/a1, b1, tc0,  /*out*/o1, tc1);
    fullAdder(/*in*/a2, b2, tc1,  /*out*/o2, tc2);
    fullAdder(/*in*/a3, b3, tc2,  /*out*/o3, overflow);
}

int main() {
    alias T = ubyte16; // ubyte32 with AVX.
    immutable T zero;
    immutable T one = ubyte.max;
    immutable T a0 = zero, a1 = one, a2 = zero, a3 = zero,
                b0 = zero, b1 = one, b2 = one,  b3 = one;
    T s0, s1, s2, s3, overflow;

    fourBitsAdder(/*in*/ a0, a1, a2, a3,
                  /*in*/ b0, b1, b2, b3,
                  /*out*/s0, s1, s2, s3, overflow);

    //writefln("      a3 %(%08b%)", a3);
    writefln("      a3 %(%08b%)", a3.array);
    writefln("      a2 %(%08b%)", a2.array);
    writefln("      a1 %(%08b%)", a1.array);
    writefln("      a0 %(%08b%)", a0.array);
    writefln("      +");
    writefln("      b3 %(%08b%)", b3.array);
    writefln("      b2 %(%08b%)", b2.array);
    writefln("      b1 %(%08b%)", b1.array);
    writefln("      b0 %(%08b%)", b0.array);
    writefln("      =");
    writefln("      s3 %(%08b%)", s3.array);
    writefln("      s2 %(%08b%)", s2.array);
    writefln("      s1 %(%08b%)", s1.array);
    writefln("      s0 %(%08b%)", s0.array);
    writefln("overflow %(%08b%)", overflow.array);
}
Output:
      a3 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
      a2 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
      a1 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
      a0 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
      +
      b3 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
      b2 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
      b1 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
      b0 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
      =
      s3 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
      s2 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
      s1 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
      s0 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
overflow 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111

Compiled by the ldc2 compiler to (where T = ubyte32, 256 adds using AVX2):

fourBitsAdder:
    pushl       %ebp
    movl        %esp,   %ebp
    andl        $-32,   %esp
    subl        $32,    %esp
    vmovaps 136(%ebp),  %ymm4
    vxorps      %ymm3,  %ymm4, %ymm5
    movl     20(%ebp),  %ecx
    vmovaps     %ymm5, (%ecx)
    vandps      %ymm3,  %ymm4, %ymm3
    vmovaps 104(%ebp),  %ymm4
    vxorps      %ymm2,  %ymm4, %ymm5
    vxorps      %ymm3,  %ymm5, %ymm6
    movl     16(%ebp),  %ecx
    vmovaps     %ymm6, (%ecx)
    vandps      %ymm3,  %ymm5, %ymm3
    vandps      %ymm2,  %ymm4, %ymm2
    vorps       %ymm2,  %ymm3, %ymm2
    vmovaps  72(%ebp),  %ymm3
    vxorps      %ymm1,  %ymm3, %ymm4
    vxorps      %ymm2,  %ymm4, %ymm5
    movl     12(%ebp),  %ecx
    vmovaps    %ymm5,  (%ecx)
    vandps      %ymm2,  %ymm4, %ymm2
    vandps      %ymm1,  %ymm3, %ymm1
    vorps       %ymm1,  %ymm2, %ymm1
    vmovaps  40(%ebp),  %ymm2
    vxorps      %ymm0,  %ymm2, %ymm3
    vxorps      %ymm1,  %ymm3, %ymm4
    movl      8(%ebp),  %ecx
    vmovaps     %ymm4, (%ecx)
    vandps      %ymm1,  %ymm3, %ymm1
    vandps      %ymm0,  %ymm2, %ymm0
    vorps       %ymm0,  %ymm1, %ymm0
    vmovaps     %ymm0, (%eax)
    movl        %ebp,   %esp
    popl        %ebp
    vzeroupper
    ret         $160

Delphi

Translation of: C#
program Four_bit_adder;

{$APPTYPE CONSOLE}

uses
  System.SysUtils;

Type
  TBitAdderOutput = record
    S, C: Boolean;
    procedure Assign(_s, _C: Boolean);
    function ToString: string;
  end;

  TNibbleBits = array[1..4] of Boolean;

  TNibble = record
    Bits: TNibbleBits;
    procedure Assign(_Bits: TNibbleBits); overload;
    procedure Assign(value: byte); overload;
    function ToString: string;
  end;

  TFourBitAdderOutput = record
    N: TNibble;
    c: Boolean;
    procedure Assign(_c: Boolean; _N: TNibbleBits);
    function ToString: string;
  end;

  TLogic = record
    class function GateNot(const A: Boolean): Boolean; static;
    class function GateAnd(const A, B: Boolean): Boolean; static;
    class function GateOr(const A, B: Boolean): Boolean; static;
    class function GateXor(const A, B: Boolean): Boolean; static;
  end;

  TConstructiveBlocks = record
    function HalfAdder(const A, B: Boolean): TBitAdderOutput;
    function FullAdder(const A, B, CI: Boolean): TBitAdderOutput;
    function FourBitAdder(const A, B: TNibble; const CI: Boolean): TFourBitAdderOutput;
  end;



{ TBitAdderOutput }

procedure TBitAdderOutput.Assign(_s, _C: Boolean);
begin
  s := _s;
  c := _C;
end;

function TBitAdderOutput.ToString: string;
begin
  Result := 'S' + ord(s).ToString + 'C' + ord(c).ToString;
end;

{ TNibble }

procedure TNibble.Assign(_Bits: TNibbleBits);
var
  i: Integer;
begin
  for i := 1 to 4 do
    Bits[i] := _Bits[i];
end;

procedure TNibble.Assign(value: byte);
var
  i: Integer;
begin
  value := value and $0F;
  for i := 1 to 4 do
    Bits[i] := ((value shr (i - 1)) and 1) = 1;
end;

function TNibble.ToString: string;
var
  i: Integer;
begin
  Result := '';
  for i := 4 downto 1 do
    Result := Result + ord(Bits[i]).ToString;
end;

{ TFourBitAdderOutput }

procedure TFourBitAdderOutput.Assign(_c: Boolean; _N: TNibbleBits);
begin
  N.Assign(_N);
  c := _c;
end;

function TFourBitAdderOutput.ToString: string;
begin
  Result := N.ToString + ' c=' + ord(c).ToString;
end;

{ TLogic }

class function TLogic.GateAnd(const A, B: Boolean): Boolean;
begin
  Result := A and B;
end;

class function TLogic.GateNot(const A: Boolean): Boolean;
begin
  Result := not A;
end;

class function TLogic.GateOr(const A, B: Boolean): Boolean;
begin
  Result := A or B;
end;

class function TLogic.GateXor(const A, B: Boolean): Boolean;
begin
  Result := GateOr(GateAnd(A, GateNot(B)), (GateAnd(GateNot(A), B)));
end;

{ TConstructiveBlocks }

function TConstructiveBlocks.FourBitAdder(const A, B: TNibble; const CI: Boolean):
  TFourBitAdderOutput;
var
  FA: array[1..4] of TBitAdderOutput;
  i: Integer;
begin
  FA[1] := FullAdder(A.Bits[1], B.Bits[1], CI);
  Result.N.Bits[1] := FA[1].S;

  for i := 2 to 4 do
  begin
    FA[i] := FullAdder(A.Bits[i], B.Bits[i], FA[i - 1].C);
    Result.N.Bits[i] := FA[i].S;
  end;
  Result.C := FA[4].C;
end;

function TConstructiveBlocks.FullAdder(const A, B, CI: Boolean): TBitAdderOutput;
var
  HA1, HA2: TBitAdderOutput;
begin
  HA1 := HalfAdder(CI, A);
  HA2 := HalfAdder(HA1.S, B);
  Result.Assign(HA2.S, TLogic.GateOr(HA1.C, HA2.C));
end;

function TConstructiveBlocks.HalfAdder(const A, B: Boolean): TBitAdderOutput;
begin
  Result.Assign(TLogic.GateXor(A, B), TLogic.GateAnd(A, B));
end;

var
  j, k: Integer;
  A, B: TNibble;
  Blocks: TConstructiveBlocks;

begin
  for k := 0 to 255 do
  begin
    A.Assign(0);
    B.Assign(0);
    for j := 0 to 7 do
    begin
      if j < 4 then
        A.Bits[j + 1] := ((1 shl j) and k) > 0
      else
        B.Bits[j + 1 - 4] := ((1 shl j) and k) > 0;
    end;

    write(A.ToString, ' + ', B.ToString, ' = ');
    Writeln(Blocks.FourBitAdder(A, B, false).ToString);
  end;
  Writeln;
  Readln;
end.
Output:
0000 + 0000 = 0000 c=0
0001 + 0000 = 0001 c=0
0010 + 0000 = 0010 c=0
0011 + 0000 = 0011 c=0
0100 + 0000 = 0100 c=0
0101 + 0000 = 0101 c=0
0110 + 0000 = 0110 c=0
0111 + 0000 = 0111 c=0
1000 + 0000 = 1000 c=0
1001 + 0000 = 1001 c=0
1010 + 0000 = 1010 c=0
1011 + 0000 = 1011 c=0
1100 + 0000 = 1100 c=0
1101 + 0000 = 1101 c=0
1110 + 0000 = 1110 c=0
1111 + 0000 = 1111 c=0
0000 + 0001 = 0001 c=0
0001 + 0001 = 0010 c=0
0010 + 0001 = 0011 c=0
0011 + 0001 = 0100 c=0
0100 + 0001 = 0101 c=0
0101 + 0001 = 0110 c=0
0110 + 0001 = 0111 c=0
0111 + 0001 = 1000 c=0
1000 + 0001 = 1001 c=0
1001 + 0001 = 1010 c=0
1010 + 0001 = 1011 c=0
1011 + 0001 = 1100 c=0
1100 + 0001 = 1101 c=0
1101 + 0001 = 1110 c=0
1110 + 0001 = 1111 c=0
1111 + 0001 = 0000 c=1
0000 + 0010 = 0010 c=0
0001 + 0010 = 0011 c=0
0010 + 0010 = 0100 c=0
0011 + 0010 = 0101 c=0
0100 + 0010 = 0110 c=0
0101 + 0010 = 0111 c=0
0110 + 0010 = 1000 c=0
0111 + 0010 = 1001 c=0
1000 + 0010 = 1010 c=0
1001 + 0010 = 1011 c=0
1010 + 0010 = 1100 c=0
1011 + 0010 = 1101 c=0
1100 + 0010 = 1110 c=0
1101 + 0010 = 1111 c=0
1110 + 0010 = 0000 c=1
1111 + 0010 = 0001 c=1
0000 + 0011 = 0011 c=0
0001 + 0011 = 0100 c=0
0010 + 0011 = 0101 c=0
0011 + 0011 = 0110 c=0
0100 + 0011 = 0111 c=0
0101 + 0011 = 1000 c=0
0110 + 0011 = 1001 c=0
0111 + 0011 = 1010 c=0
1000 + 0011 = 1011 c=0
1001 + 0011 = 1100 c=0
1010 + 0011 = 1101 c=0
1011 + 0011 = 1110 c=0
1100 + 0011 = 1111 c=0
1101 + 0011 = 0000 c=1
1110 + 0011 = 0001 c=1
1111 + 0011 = 0010 c=1
0000 + 0100 = 0100 c=0
0001 + 0100 = 0101 c=0
0010 + 0100 = 0110 c=0
0011 + 0100 = 0111 c=0
0100 + 0100 = 1000 c=0
0101 + 0100 = 1001 c=0
0110 + 0100 = 1010 c=0
0111 + 0100 = 1011 c=0
1000 + 0100 = 1100 c=0
1001 + 0100 = 1101 c=0
1010 + 0100 = 1110 c=0
1011 + 0100 = 1111 c=0
1100 + 0100 = 0000 c=1
1101 + 0100 = 0001 c=1
1110 + 0100 = 0010 c=1
1111 + 0100 = 0011 c=1
0000 + 0101 = 0101 c=0
0001 + 0101 = 0110 c=0
0010 + 0101 = 0111 c=0
0011 + 0101 = 1000 c=0
0100 + 0101 = 1001 c=0
0101 + 0101 = 1010 c=0
0110 + 0101 = 1011 c=0
0111 + 0101 = 1100 c=0
1000 + 0101 = 1101 c=0
1001 + 0101 = 1110 c=0
1010 + 0101 = 1111 c=0
1011 + 0101 = 0000 c=1
1100 + 0101 = 0001 c=1
1101 + 0101 = 0010 c=1
1110 + 0101 = 0011 c=1
1111 + 0101 = 0100 c=1
0000 + 0110 = 0110 c=0
0001 + 0110 = 0111 c=0
0010 + 0110 = 1000 c=0
0011 + 0110 = 1001 c=0
0100 + 0110 = 1010 c=0
0101 + 0110 = 1011 c=0
0110 + 0110 = 1100 c=0
0111 + 0110 = 1101 c=0
1000 + 0110 = 1110 c=0
1001 + 0110 = 1111 c=0
1010 + 0110 = 0000 c=1
1011 + 0110 = 0001 c=1
1100 + 0110 = 0010 c=1
1101 + 0110 = 0011 c=1
1110 + 0110 = 0100 c=1
1111 + 0110 = 0101 c=1
0000 + 0111 = 0111 c=0
0001 + 0111 = 1000 c=0
0010 + 0111 = 1001 c=0
0011 + 0111 = 1010 c=0
0100 + 0111 = 1011 c=0
0101 + 0111 = 1100 c=0
0110 + 0111 = 1101 c=0
0111 + 0111 = 1110 c=0
1000 + 0111 = 1111 c=0
1001 + 0111 = 0000 c=1
1010 + 0111 = 0001 c=1
1011 + 0111 = 0010 c=1
1100 + 0111 = 0011 c=1
1101 + 0111 = 0100 c=1
1110 + 0111 = 0101 c=1
1111 + 0111 = 0110 c=1
0000 + 1000 = 1000 c=0
0001 + 1000 = 1001 c=0
0010 + 1000 = 1010 c=0
0011 + 1000 = 1011 c=0
0100 + 1000 = 1100 c=0
0101 + 1000 = 1101 c=0
0110 + 1000 = 1110 c=0
0111 + 1000 = 1111 c=0
1000 + 1000 = 0000 c=1
1001 + 1000 = 0001 c=1
1010 + 1000 = 0010 c=1
1011 + 1000 = 0011 c=1
1100 + 1000 = 0100 c=1
1101 + 1000 = 0101 c=1
1110 + 1000 = 0110 c=1
1111 + 1000 = 0111 c=1
0000 + 1001 = 1001 c=0
0001 + 1001 = 1010 c=0
0010 + 1001 = 1011 c=0
0011 + 1001 = 1100 c=0
0100 + 1001 = 1101 c=0
0101 + 1001 = 1110 c=0
0110 + 1001 = 1111 c=0
0111 + 1001 = 0000 c=1
1000 + 1001 = 0001 c=1
1001 + 1001 = 0010 c=1
1010 + 1001 = 0011 c=1
1011 + 1001 = 0100 c=1
1100 + 1001 = 0101 c=1
1101 + 1001 = 0110 c=1
1110 + 1001 = 0111 c=1
1111 + 1001 = 1000 c=1
0000 + 1010 = 1010 c=0
0001 + 1010 = 1011 c=0
0010 + 1010 = 1100 c=0
0011 + 1010 = 1101 c=0
0100 + 1010 = 1110 c=0
0101 + 1010 = 1111 c=0
0110 + 1010 = 0000 c=1
0111 + 1010 = 0001 c=1
1000 + 1010 = 0010 c=1
1001 + 1010 = 0011 c=1
1010 + 1010 = 0100 c=1
1011 + 1010 = 0101 c=1
1100 + 1010 = 0110 c=1
1101 + 1010 = 0111 c=1
1110 + 1010 = 1000 c=1
1111 + 1010 = 1001 c=1
0000 + 1011 = 1011 c=0
0001 + 1011 = 1100 c=0
0010 + 1011 = 1101 c=0
0011 + 1011 = 1110 c=0
0100 + 1011 = 1111 c=0
0101 + 1011 = 0000 c=1
0110 + 1011 = 0001 c=1
0111 + 1011 = 0010 c=1
1000 + 1011 = 0011 c=1
1001 + 1011 = 0100 c=1
1010 + 1011 = 0101 c=1
1011 + 1011 = 0110 c=1
1100 + 1011 = 0111 c=1
1101 + 1011 = 1000 c=1
1110 + 1011 = 1001 c=1
1111 + 1011 = 1010 c=1
0000 + 1100 = 1100 c=0
0001 + 1100 = 1101 c=0
0010 + 1100 = 1110 c=0
0011 + 1100 = 1111 c=0
0100 + 1100 = 0000 c=1
0101 + 1100 = 0001 c=1
0110 + 1100 = 0010 c=1
0111 + 1100 = 0011 c=1
1000 + 1100 = 0100 c=1
1001 + 1100 = 0101 c=1
1010 + 1100 = 0110 c=1
1011 + 1100 = 0111 c=1
1100 + 1100 = 1000 c=1
1101 + 1100 = 1001 c=1
1110 + 1100 = 1010 c=1
1111 + 1100 = 1011 c=1
0000 + 1101 = 1101 c=0
0001 + 1101 = 1110 c=0
0010 + 1101 = 1111 c=0
0011 + 1101 = 0000 c=1
0100 + 1101 = 0001 c=1
0101 + 1101 = 0010 c=1
0110 + 1101 = 0011 c=1
0111 + 1101 = 0100 c=1
1000 + 1101 = 0101 c=1
1001 + 1101 = 0110 c=1
1010 + 1101 = 0111 c=1
1011 + 1101 = 1000 c=1
1100 + 1101 = 1001 c=1
1101 + 1101 = 1010 c=1
1110 + 1101 = 1011 c=1
1111 + 1101 = 1100 c=1
0000 + 1110 = 1110 c=0
0001 + 1110 = 1111 c=0
0010 + 1110 = 0000 c=1
0011 + 1110 = 0001 c=1
0100 + 1110 = 0010 c=1
0101 + 1110 = 0011 c=1
0110 + 1110 = 0100 c=1
0111 + 1110 = 0101 c=1
1000 + 1110 = 0110 c=1
1001 + 1110 = 0111 c=1
1010 + 1110 = 1000 c=1
1011 + 1110 = 1001 c=1
1100 + 1110 = 1010 c=1
1101 + 1110 = 1011 c=1
1110 + 1110 = 1100 c=1
1111 + 1110 = 1101 c=1
0000 + 1111 = 1111 c=0
0001 + 1111 = 0000 c=1
0010 + 1111 = 0001 c=1
0011 + 1111 = 0010 c=1
0100 + 1111 = 0011 c=1
0101 + 1111 = 0100 c=1
0110 + 1111 = 0101 c=1
0111 + 1111 = 0110 c=1
1000 + 1111 = 0111 c=1
1001 + 1111 = 1000 c=1
1010 + 1111 = 1001 c=1
1011 + 1111 = 1010 c=1
1100 + 1111 = 1011 c=1
1101 + 1111 = 1100 c=1
1110 + 1111 = 1101 c=1
1111 + 1111 = 1110 c=1

EasyLang

proc xor a b . r .
   na = bitand bitnot a 1
   nb = bitand bitnot b 1
   r = bitor bitand a nb bitand b na
.
proc half_add a b . s c .
   xor a b s
   c = bitand a b
.
proc full_add a b c . s g .
   half_add a c x y
   half_add x b s z
   g = bitor y z
.
proc bit4add a4 a3 a2 a1 b4 b3 b2 b1 . s4 s3 s2 s1 c .
   full_add a1 b1 0 s1 c
   full_add a2 b2 c s2 c
   full_add a3 b3 c s3 c
   full_add a4 b4 c s4 c
.
write "1101 + 1011 = "
bit4add 1 1 0 1 1 0 1 1 s4 s3 s2 s1 c
print c & s4 & s3 & s2 & s1
Output:
1101 + 1011 = 11000

Elixir

Works with: Elixir version 1.1
Translation of: Ruby
defmodule RC do
  use Bitwise
  @bit_size 4
  
  def four_bit_adder(a, b) do           # returns pair {sum, carry}
    a_bits = binary_string_to_bits(a)
    b_bits = binary_string_to_bits(b)
    Enum.zip(a_bits, b_bits)
    |> List.foldr({[], 0}, fn {a_bit, b_bit}, {acc, carry} ->
         {s, c} = full_adder(a_bit, b_bit, carry)
         {[s | acc], c}
       end)
  end
  
  defp full_adder(a, b, c0) do
    {s, c} = half_adder(c0, a)
    {s, c1} = half_adder(s, b)
    {s, bor(c, c1)}                     # returns pair {sum, carry}
  end
  
  defp half_adder(a, b) do
    {bxor(a, b), band(a, b)}            # returns pair {sum, carry}
  end
  
  def int_to_binary_string(n) do
    Integer.to_string(n,2) |> String.rjust(@bit_size, ?0)
  end
  
  defp binary_string_to_bits(s) do
    String.codepoints(s) |> Enum.map(fn bit -> String.to_integer(bit) end)
  end
  
  def task do
    IO.puts " A    B      A      B   C    S  sum" 
    Enum.each(0..15, fn a ->
      bin_a = int_to_binary_string(a)
      Enum.each(0..15, fn b ->
        bin_b = int_to_binary_string(b)
        {sum, carry} = four_bit_adder(bin_a, bin_b)
        :io.format "~2w + ~2w = ~s + ~s = ~w ~s = ~2w~n",
            [a, b, bin_a, bin_b, carry, Enum.join(sum), Integer.undigits([carry | sum], 2)]
      end)
    end)
  end
end

RC.task
Output:
 A    B      A      B   C    S  sum
 0 +  0 = 0000 + 0000 = 0 0000 =  0
 0 +  1 = 0000 + 0001 = 0 0001 =  1
 0 +  2 = 0000 + 0010 = 0 0010 =  2
 0 +  3 = 0000 + 0011 = 0 0011 =  3
 0 +  4 = 0000 + 0100 = 0 0100 =  4
...
 7 + 13 = 0111 + 1101 = 1 0100 = 20
 7 + 14 = 0111 + 1110 = 1 0101 = 21
 7 + 15 = 0111 + 1111 = 1 0110 = 22
 8 +  0 = 1000 + 0000 = 0 1000 =  8
 8 +  1 = 1000 + 0001 = 0 1001 =  9
 8 +  2 = 1000 + 0010 = 0 1010 = 10
...
15 + 12 = 1111 + 1100 = 1 1011 = 27
15 + 13 = 1111 + 1101 = 1 1100 = 28
15 + 14 = 1111 + 1110 = 1 1101 = 29
15 + 15 = 1111 + 1111 = 1 1110 = 30

Erlang

Yes, it is misleading to have a "choose your own number of bits" adder in the four_bit_adder module. But it does make it easier to find the module from the Rosettacode task name.

-module( four_bit_adder ).

-export( [add_bits/3, create/1, task/0] ).

add_bits( Adder, A_bits, B_bits ) ->
	Adder ! {erlang:self(), lists:reverse(A_bits), lists:reverse(B_bits)},
	receive
	{Adder, Sum, Carry} -> {Sum, Carry}
	end.

create( How_many_bits ) ->
	Full_adders = connect_full_adders( [full_adder_create() || _X <- lists:seq(1, How_many_bits)] ),
	erlang:spawn_link( fun() -> bit_adder_loop( Full_adders ) end ).

task() ->
	Adder = create( 4 ),
	add_bits( Adder, [0,0,1,0], [0,0,1,1] ).



bit_adder_loop( Full_adders ) ->
	receive
	{Pid, As, Bs} ->
		Sum = [full_adder_sum(Adder, A, B) || {Adder, A, B} <- lists:zip3(Full_adders, As, Bs)],
		Carry = receive
			{carry, C} -> C
			end,
		Pid ! {erlang:self(), lists:reverse(Sum), Carry},
		bit_adder_loop( Full_adders )
	end.

connect_full_adders( [Full_adder | T]=Full_adders ) ->
	lists:foldl( fun connect_full_adders/2, Full_adder, T ),
	Full_adders.

connect_full_adders( Full_adder, Previous_full_adder ) ->
	Previous_full_adder ! {carry_to, Full_adder},
	Full_adder.

half_adder( A, B ) -> {z_xor(A, B), A band B}.

full_adder( A, B, Carry ) ->
	{Sum1, Carry1} = half_adder( A, Carry),
	{Sum, Carry2} = half_adder( B, Sum1),
	{Sum, Carry1 bor Carry2}.

full_adder_create( ) -> erlang:spawn( fun() -> full_adder_loop({0, no_carry_pid}) end ).

full_adder_loop( {Carry, Carry_to} ) ->
	receive
	{carry, New_carry} -> full_adder_loop( {New_carry, Carry_to} );
	{carry_to, Pid} -> full_adder_loop( {Carry, Pid} );
	{add, Pid, A, B} ->
		{Sum, New_carry} = full_adder( A, B, Carry ),
		Pid ! {sum, erlang:self(), Sum},
		full_adder_loop_carry_pid( Carry_to, Pid ) ! {carry, New_carry},
		full_adder_loop( {New_carry, Carry_to} )
	end.

full_adder_loop_carry_pid( no_carry_pid, Pid ) -> Pid;
full_adder_loop_carry_pid( Pid, _Pid ) -> Pid.

full_adder_sum( Pid, A, B ) ->
	Pid ! {add, erlang:self(), A, B},
	receive
	{sum, Pid, S} -> S
	end.

%% xor exists, this is another implementation.
z_xor( A, B ) -> (A band (2+bnot B)) bor ((2+bnot A) band B).
Output:
28> four_bit_adder:task().
{[0,1,0,1],0}

F#

type Bit =
    | Zero
    | One

let bNot = function
    | Zero -> One
    | One -> Zero

let bAnd a b =
    match (a, b) with
    | (One, One) -> One
    | _ -> Zero

let bOr a b =
    match (a, b) with
    | (Zero, Zero) -> Zero
    | _ -> One

let bXor a b = bAnd (bOr a b) (bNot (bAnd a b))

let bHA a b = bAnd a b, bXor a b

let bFA a b cin =
    let (c0, s0) = bHA a b
    let (c1, s1) = bHA s0 cin
    (bOr c0 c1, s1)

let b4A (a3, a2, a1, a0) (b3, b2, b1, b0) =
    let (c1, s0) = bFA a0 b0 Zero
    let (c2, s1) = bFA a1 b1 c1
    let (c3, s2) = bFA a2 b2 c2
    let (c4, s3) = bFA a3 b3 c3
    (c4, s3, s2, s1, s0)

printfn "0001 + 0111 ="
b4A (Zero, Zero, Zero, One) (Zero, One, One, One) |> printfn "%A"
Output:
0001 + 0111 =
(Zero, One, Zero, Zero, 

Forth

: "NOT" invert 1 and ;
: "XOR" over over "NOT" and >r swap "NOT" and r> or ;
: halfadder over over and >r "XOR" r> ;
: fulladder halfadder >r swap halfadder r> or ;

: 4bitadder                            ( a3 a2 a1 a0 b3 b2 b1 b0 -- r3 r2 r1 r0 c)
  4 roll 0  fulladder swap >r >r
  3 roll r> fulladder swap >r >r
  2 roll r> fulladder swap >r fulladder r> r> r> 3 roll
;

: .add4 4bitadder 0 .r 4 0 do i 3 - abs roll 0 .r loop cr ;
Output:
1 1 0 0     0 0 1 1  .add4 01111
 ok

Fortran

Works with: Fortran version 90 and later
module logic
  implicit none

contains

function xor(a, b)
  logical :: xor
  logical, intent(in) :: a, b

  xor = (a .and. .not. b) .or. (b .and. .not. a)
end function xor

function halfadder(a, b, c)
  logical :: halfadder
  logical, intent(in)  :: a, b
  logical, intent(out) :: c

  halfadder = xor(a, b)
  c = a .and. b
end function halfadder

function fulladder(a, b, c0, c1)
  logical :: fulladder
  logical, intent(in)  :: a, b, c0
  logical, intent(out) :: c1
  logical :: c2, c3

  fulladder = halfadder(halfadder(c0, a, c2), b, c3)
  c1 = c2 .or. c3
end function fulladder

subroutine fourbitadder(a, b, s)
  logical, intent(in)  :: a(0:3), b(0:3)
  logical, intent(out) :: s(0:4)
  logical :: c0, c1, c2

  s(0) = fulladder(a(0), b(0), .false., c0)  
  s(1) = fulladder(a(1), b(1), c0, c1)
  s(2) = fulladder(a(2), b(2), c1, c2)
  s(3) = fulladder(a(3), b(3), c2, s(4))
end subroutine fourbitadder
end module

program Four_bit_adder
  use logic
  implicit none
  
  logical, dimension(0:3) :: a, b
  logical, dimension(0:4) :: s
  integer, dimension(0:3) :: ai, bi
  integer, dimension(0:4) :: si
  integer :: i, j

  do i = 0, 15
    a(0) = btest(i, 0); a(1) = btest(i, 1); a(2) = btest(i, 2); a(3) = btest(i, 3)
    where(a)
      ai = 1
    else where
      ai = 0
    end where
    do j = 0, 15
      b(0) = btest(j, 0); b(1) = btest(j, 1); b(2) = btest(j, 2); b(3) = btest(j, 3)
      where(b)
        bi = 1
      else where
        bi = 0
      end where
      call fourbitadder(a, b, s)
      where (s)
        si = 1
      elsewhere
        si = 0
      end where
      write(*, "(4i1,a,4i1,a,5i1)") ai(3:0:-1), " + ", bi(3:0:-1), " = ", si(4:0:-1)
    end do
  end do  
end program
Output:

(selected)

1100 + 1100 = 11000
1100 + 1101 = 11001
1100 + 1110 = 11010
1100 + 1111 = 11011
1101 + 0000 = 01101
1101 + 0001 = 01110
1101 + 0010 = 01111
1101 + 0011 = 10000

Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website.

In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.

Solution

Testing with all the (256) possible combinations:

  :

FreeBASIC

sub half_add( byval a as ubyte, byval b as ubyte,_
              byref s as ubyte, byref c as ubyte)
    s = a xor b
    c = a and b
end sub

sub full_add( byval a as ubyte, byval b as ubyte, byval c as ubyte,_
              byref s as ubyte, byref g as ubyte )
    dim as ubyte x, y, z
    half_add( a, c, x, y )
    half_add( x, b, s, z )
    g = y or z
end sub

sub fourbit_add( byval a3 as ubyte, byval a2 as ubyte, byval a1 as ubyte, byval a0 as ubyte,_
                 byval b3 as ubyte, byval b2 as ubyte, byval b1 as ubyte, byval b0 as ubyte,_
                 byref s3 as ubyte, byref s2 as ubyte, byref s1 as ubyte, byref s0 as ubyte,_
                 byref carry as ubyte )
    dim as ubyte c2, c1, c0
    full_add(a0, b0,  0, s0, c0)
    full_add(a1, b1, c0, s1, c1)
    full_add(a2, b2, c1, s2, c2)
    full_add(a3, b3, c2, s3, carry )
end sub

dim as ubyte s3, s2, s1, s0, carry

print "1100 + 0011 = ";
fourbit_add( 1, 1, 0, 0,  0, 0, 1, 1,  s3, s2, s1, s0, carry )
print carry;s3;s2;s1;s0

print "1111 + 0001 = ";
fourbit_add( 1, 1, 1, 1,  0, 0, 0, 1,  s3, s2, s1, s0, carry )
print carry;s3;s2;s1;s0

print "1111 + 1111 = ";
fourbit_add( 1, 1, 1, 1,  1, 1, 1, 1,  s3, s2, s1, s0, carry )
print carry;s3;s2;s1;s0
Output:

1100 + 0011 = 01111 1111 + 0001 = 10000 1111 + 1111 = 11110

Go

Bytes

Go does not have a bit type, so byte is used. This is the straightforward solution using bytes and functions.

package main

import "fmt"

func xor(a, b byte) byte {
    return a&(^b) | b&(^a)
}

func ha(a, b byte) (s, c byte) {
    return xor(a, b), a & b
}

func fa(a, b, c0 byte) (s, c1 byte) {
    sa, ca := ha(a, c0)
    s, cb := ha(sa, b)
    c1 = ca | cb
    return
}

func add4(a3, a2, a1, a0, b3, b2, b1, b0 byte) (v, s3, s2, s1, s0 byte) {
    s0, c0 := fa(a0, b0, 0)
    s1, c1 := fa(a1, b1, c0)
    s2, c2 := fa(a2, b2, c1)
    s3, v = fa(a3, b3, c2)
    return
}

func main() {
    // add 10+9  result should be 1 0 0 1 1
    fmt.Println(add4(1, 0, 1, 0, 1, 0, 0, 1))
}
Output:
1 0 0 1 1

Channels

Alternative solution is a little more like a simulation.

package main

import "fmt"

// A wire is modeled as a channel of booleans.
// You can feed it a single value without blocking.
// Reading a value blocks until a value is available.
type Wire chan bool

func MkWire() Wire {
	return make(Wire, 1)
}

// A source for zero values.
func Zero() (r Wire) {
	r = MkWire()
	go func() {
		for {
			r <- false
		}
	}()
	return
}

// And gate.
func And(a, b Wire) (r Wire) {
	r = MkWire()
	go func() {
		for {
			r <- (<-a && <-b)
		}
	}()
	return
}

// Or gate.
func Or(a, b Wire) (r Wire) {
	r = MkWire()
	go func() {
		for {
			r <- (<-a || <-b)
		}
	}()
	return
}

// Not gate.
func Not(a Wire) (r Wire) {
	r = MkWire()
	go func() {
		for {
			r <- !(<-a)
		}
	}()
	return
}

// Split a wire in two.
func Split(a Wire) (Wire, Wire) {
	r1 := MkWire()
	r2 := MkWire()
	go func() {
		for {
			x := <-a
			r1 <- x
			r2 <- x
		}
	}()
	return r1, r2
}

// Xor gate, composed of Or, And and Not gates.
func Xor(a, b Wire) Wire {
	a1, a2 := Split(a)
	b1, b2 := Split(b)
	return Or(And(Not(a1), b1), And(a2, Not(b2)))
}

// A half adder, composed of two splits and an And and Xor gate.
func HalfAdder(a, b Wire) (sum, carry Wire) {
	a1, a2 := Split(a)
	b1, b2 := Split(b)
	carry = And(a1, b1)
	sum = Xor(a2, b2)
	return
}

// A full adder, composed of two half adders, and an Or gate.
func FullAdder(a, b, carryIn Wire) (result, carryOut Wire) {
	s1, c1 := HalfAdder(carryIn, a)
	result, c2 := HalfAdder(b, s1)
	carryOut = Or(c1, c2)
	return
}

// A four bit adder, composed of a zero source, and four full adders.
func FourBitAdder(a1, a2, a3, a4 Wire, b1, b2, b3, b4 Wire) (r1, r2, r3, r4 Wire, carry Wire) {
	carry = Zero()
	r1, carry = FullAdder(a1, b1, carry)
	r2, carry = FullAdder(a2, b2, carry)
	r3, carry = FullAdder(a3, b3, carry)
	r4, carry = FullAdder(a4, b4, carry)
	return
}

func main() {
	// Create wires
	a1, a2, a3, a4 := MakeWire(), MakeWire(), MakeWire(), MakeWire()
	b1, b2, b3, b4 := MakeWire(), MakeWire(), MakeWire(), MakeWire()
	// Construct circuit
	r1, r2, r3, r4, carry := FourBitAdder(a1, a2, a3, a4, b1, b2, b3, b4)
	// Feed it some values
	a4 <- false
	a3 <- false
	a2 <- true
	a1 <- false // 0010
	b4 <- true
	b3 <- true
	b2 <- true
	b1 <- false // 1110
	B := map[bool]int{false: 0, true: 1}
	// Read the result
	fmt.Printf("0010 + 1110 = %d%d%d%d (carry = %d)\n",
		B[<-r4], B[<-r3], B[<-r2], B[<-r1], B[<-carry])
}

Mini reference:

  • "channel <- value" sends a value to a channel. Blocks if its buffer is full.
  • "<-channel" reads a value from a channel. Blocks if its buffer is empty.
  • "go function()" creates and runs a go-rountine. It will continue executing concurrently.

Groovy

class Main {
    static void main(args) {

        def bit1, bit2, bit3, bit4, carry

        def fourBitAdder = new FourBitAdder(
                { value -> bit1 = value },
                { value -> bit2 = value },
                { value -> bit3 = value },
                { value -> bit4 = value },
                { value -> carry = value }
        )

        // 5 + 6 = 11

        // 0101 i.e. 5
        fourBitAdder.setNum1Bit1 false
        fourBitAdder.setNum1Bit2 true
        fourBitAdder.setNum1Bit3 false
        fourBitAdder.setNum1Bit4 true

        // 0110 i.e 6
        fourBitAdder.setNum2Bit1 false
        fourBitAdder.setNum2Bit2 true
        fourBitAdder.setNum2Bit3 true
        fourBitAdder.setNum2Bit4 false

        def boolToInt = { bool ->
            bool ? 1 : 0
        }

        println ("0101 + 0110 = ${boolToInt(bit1)}${boolToInt(bit2)}${boolToInt(bit3)}${boolToInt(bit4)}")
    }
}

class Not {
    Closure output

    Not(output) {
        this.output = output
    }

    def setInput(input) {
        output !input
    }
}

class And {
    boolean input1
    boolean input2
    Closure output

    And(output) {
        this.output = output
    }

    def setInput1(input) {
        this.input1 = input
        output(input1 && input2)
    }

    def setInput2(input) {
        this.input2 = input
        output(input1 && input2)
    }
}

class Nand {
    And andGate
    Not notGate

    Nand(output) {
        notGate = new Not(output)
        andGate = new And({ value ->
            notGate.setInput value
        })
    }

    def setInput1(input) {
        andGate.setInput1 input
    }

    def setInput2(input) {
        andGate.setInput2 input
    }
}

class Or {
    Not firstInputNegation
    Not secondInputNegation
    Nand nandGate

    Or(output) {
        nandGate = new Nand(output)
        firstInputNegation = new Not({ value ->
            nandGate.setInput1 value
        })
        secondInputNegation = new Not({ value ->
            nandGate.setInput2 value
        })
    }

    def setInput1(input) {
        firstInputNegation.setInput input
    }

    def setInput2(input) {
        secondInputNegation.setInput input
    }
}

class Xor {
    And andGate
    Or orGate
    Nand nandGate

    Xor(output) {
        andGate = new And(output)
        orGate = new Or({ value ->
            andGate.setInput1 value
        })
        nandGate = new Nand({ value ->
            andGate.setInput2 value
        })

    }

    def setInput1(input) {
        orGate.setInput1 input
        nandGate.setInput1 input
    }

    def setInput2(input) {
        orGate.setInput2 input
        nandGate.setInput2 input
    }
}

class Adder {
    Or orGate
    Xor xorGate1
    Xor xorGate2
    And andGate1
    And andGate2

    Adder(sumOutput, carryOutput) {
        xorGate1 = new Xor(sumOutput)
        orGate = new Or(carryOutput)
        andGate1 = new And({ value ->
            orGate.setInput1 value
        })
        xorGate2 = new Xor({ value ->
            andGate1.setInput1 value
            xorGate1.setInput1 value
        })
        andGate2 = new And({ value ->
            orGate.setInput2 value
        })
    }

    def setBit1(input) {
        xorGate2.setInput1 input
        andGate2.setInput2 input
    }

    def setBit2(input) {
        xorGate2.setInput2 input
        andGate2.setInput1 input
    }

    def setCarry(input) {
        andGate1.setInput2 input
        xorGate1.setInput2 input
    }
}

class FourBitAdder {
    Adder adder1
    Adder adder2
    Adder adder3
    Adder adder4

    FourBitAdder(bit1, bit2, bit3, bit4, carry) {
        adder1 = new Adder(bit1, carry)
        adder2 = new Adder(bit2, { value ->
            adder1.setCarry value
        })
        adder3 = new Adder(bit3, { value ->
            adder2.setCarry value
        })
        adder4 = new Adder(bit4, { value ->
            adder3.setCarry value
        })
    }

    def setNum1Bit1(input) {
        adder1.setBit1 input
    }

    def setNum1Bit2(input) {
        adder2.setBit1 input
    }

    def setNum1Bit3(input) {
        adder3.setBit1 input
    }

    def setNum1Bit4(input) {
        adder4.setBit1 input
    }

    def setNum2Bit1(input) {
        adder1.setBit2 input
    }

    def setNum2Bit2(input) {
        adder2.setBit2 input
    }

    def setNum2Bit3(input) {
        adder3.setBit2 input
    }

    def setNum2Bit4(input) {
        adder4.setBit2 input
    }
}

Haskell

Basic gates:

import Control.Arrow
import Data.List (mapAccumR)

bor, band :: Int -> Int -> Int
bor = max
band = min
bnot :: Int -> Int
bnot = (1-)

Gates built with basic ones:

nand, xor :: Int -> Int -> Int
nand = (bnot.).band
xor a b = uncurry nand. (nand a &&& nand b) $ nand a b

Adder circuits:

halfAdder = uncurry band &&& uncurry xor 
fullAdder (c, a, b) =  (\(cy,s) ->  first (bor cy) $ halfAdder (b, s)) $ halfAdder (c, a)

adder4 as = mapAccumR (\cy (f,a,b) -> f (cy,a,b)) 0 . zip3 (replicate 4 fullAdder) as

Example using adder4

*Main> adder4 [1,0,1,0] [1,1,1,1]
(1,[1,0,0,1])

Icon and Unicon

Based on the algorithms shown in the Fortran entry, but Unicon does not allow pass by reference for immutable types, so a small carry record is used instead.

#
# 4bitadder.icn, emulate a 4 bit adder. Using only and, or, not
#
record carry(c)

#
# excercise the adder, either "test" or 2 numbers
#
procedure main(argv)
    c := carry(0)

    # cli test
    if map(\argv[1]) == "test" then {
        # Unicon allows explicit radix literals
        every i := (2r0000  | 2r1001 | 2r1111) do {
            write(i, "+0,3,9,15")
            every j := (0 | 3 | 9 | 15) do {
                ans := fourbitadder(t1 := fourbits(i), t2 := fourbits(j), c)
                write(t1, " + ", t2, " = ", c.c, ":", ans)
            }
        }
        return
    }
    # command line, two values, if given, first try four bit binaries
    cli := fourbitadder(t1 := (*\argv[1] = 4 & fourbits("2r" || argv[1])),
                        t2 := (*\argv[2] = 4 & fourbits("2r" || argv[2])), c)
    write(t1, " + ", t2, " = ", c.c, ":", \cli) & return

    # if no result for that, try decimal values
    cli := fourbitadder(t1 := fourbits(\argv[1]),
                        t2 := fourbits(\argv[2]), c)
    write(t1, " + ", t2, " = ", c.c, ":", \cli) & return

    # or display the help
    write("Usage: 4bitadder [\"test\"] | [bbbb bbbb] | [n n], range 0-15")
end

#
# integer to fourbits as string
#
procedure fourbits(i)
    local s, t
    if not numeric(i) then fail
    if not (0 <= integer(i) < 16) then {
        write("out of range: ", i)
        fail
    }
    s := ""
    every t := (8 | 4 | 2 | 1) do {
        s ||:= if iand(i, t) ~= 0 then "1" else "0"
    }
    return s
end

#
# low level xor emulation with or, and, not
#
procedure xor(a, b)
    return ior(iand(a, icom(b)), iand(b, icom(a)))
end

#
# half adder, and into carry, xor for result bit
#
procedure halfadder(a, b, carry)
    carry.c := iand(a,b)
    return xor(a,b)
end

#
# full adder, two half adders, or for carry
#
procedure fulladder(a, b, c0, c1)
    local c2, c3, r
    c2 := carry(0)
    c3 := carry(0)

    # connect two half adders with carry
    r := halfadder(halfadder(c0.c, a, c2), b, c3)
    c1.c := ior(c2.c, c3.c)
    return r
end

#
# fourbit adder, as bit string
#
procedure fourbitadder(a, b, cr)
    local cs, c0, c1, c2, s
    cs := carry(0)
    c0 := carry(0)
    c1 := carry(0)
    c2 := carry(0)

    # create a string for subscripting. strings are immutable, new strings created
    s := "0000"
    # bit 0 is string position 4
    s[4+:1] := fulladder(a[4+:1], b[4+:1], cs, c0)
    s[3+:1] := fulladder(a[3+:1], b[3+:1], c0, c1)
    s[2+:1] := fulladder(a[2+:1], b[2+:1], c1, c2)
    s[1+:1] := fulladder(a[1+:1], b[1+:1], c2, cr)
    # cr.c is the overflow carry
    return s
end
Output:
prompt$ unicon -s 4bitadder.icn -x 0111 0011
0111 + 0011 = 0:1010
prompt$ ./4bitadder 13 13
1101 + 1101 = 1:1010
prompt$ ./4bitadder test
0+0,3,9,15
0000 + 0000 = 0:0000
0000 + 0011 = 0:0011
0000 + 1001 = 0:1001
0000 + 1111 = 0:1111
9+0,3,9,15
1001 + 0000 = 0:1001
1001 + 0011 = 0:1100
1001 + 1001 = 1:0010
1001 + 1111 = 1:1000
15+0,3,9,15
1111 + 0000 = 0:1111
1111 + 0011 = 1:0010
1111 + 1001 = 1:1000
1111 + 1111 = 1:1110

J

Implementation

and=: *.
or=: +.
not=: -.
xor=: (and not) or (and not)~
hadd=: and ,"0 xor
add=: ((({.,0:)@[ or {:@[ hadd {.@]), }.@])/@hadd

Example use

   1 1 1 1 add 0 1 1 1
1 0 1 1 0

To produce all results:

   add"1/~#:i.16

This will produce a 16 by 16 by 5 array, the first axis being the left argument (representing values 0..15), the second axis the right argument and the final axis being the bit indices (carry, 8, 4, 2, 1). In other words, the result is something like:

   ,"2 ' ',"1 -.&' '@":"1 add"1/~#:i.16
 00000 00001 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111
 00001 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000
 00010 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001
 00011 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010
 00100 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011
 00101 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100
 00110 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101
 00111 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110
 01000 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111
 01001 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000
 01010 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001
 01011 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010
 01100 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011
 01101 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100
 01110 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101
 01111 10000 10001 10010 10011 10100 10101 10110 10111 11000 11001 11010 11011 11100 11101 11110

Alternatively, the fact that add was designed to operate on lists of bits could have been incorporated into its definition:

add=: ((({.,0:)@[ or {:@[ hadd {.@]), }.@])/@hadd"1

Then to get all results you could use:

   add/~#:i.16

Compare this to a regular addition table:

   +/~i.10

(this produces a 10 by 10 array -- the results have no further internal array structure, though of course in the machine implementation integers can be thought of as being represented as fixed width lists of bits.)

Glossary

  ~: xor
  {. first
  }. rest
  {: last
  [  left (result is left argument)
  ]  right (result is right argument)
  0: verb which always has the result 0
  ,  combine sequences

Grammar

  u v w   these letters represent verbs such as and or or not
  x y     these letters represent nouns such as 1 or 0
  u@v     function composition
  x u~ y  reverse arguments for u (y u x)
  u/ y    reduction (u is verb between each item in y)
  u"0     u applies to the smallest elements of its argument

Also:

  x (u v) y

produces the same result as

  x u v y

while

  x (u v w) y

produces the same result as

  (x u y) v (x w y)

and

  x (u1 u2 u3 u4 u5) y

produces the the same result as

  x (u1 u2 (u3 u4 u5)) y

See also: "A Formal Description of System/360” by Adin Falkoff

Java

public class GateLogic
{
  // Basic gate interfaces
  public interface OneInputGate
  {  boolean eval(boolean input);  }
  
  public interface TwoInputGate
  {  boolean eval(boolean input1, boolean input2);  }
  
  public interface MultiGate
  {  boolean[] eval(boolean... inputs);  }
  
  // Create NOT
  public static OneInputGate NOT = new OneInputGate() {
    public boolean eval(boolean input)
    {  return !input;  }
  };
  
  // Create AND
  public static TwoInputGate AND = new TwoInputGate() {
    public boolean eval(boolean input1, boolean input2)
    {  return input1 && input2;  }
  };
  
  // Create OR
  public static TwoInputGate OR = new TwoInputGate() {
    public boolean eval(boolean input1, boolean input2)
    {  return input1 || input2;  }
  };
  
  // Create XOR
  public static TwoInputGate XOR = new TwoInputGate() {
    public boolean eval(boolean input1, boolean input2)
    {
      return OR.eval(
               AND.eval(input1, NOT.eval(input2)),
               AND.eval(NOT.eval(input1), input2)
             );
    }
  };
  
  // Create HALF_ADDER
  public static MultiGate HALF_ADDER = new MultiGate() {
    public boolean[] eval(boolean... inputs)
    {
      if (inputs.length != 2)
        throw new IllegalArgumentException();
      return new boolean[] {
        XOR.eval(inputs[0], inputs[1]),  // Output bit
        AND.eval(inputs[0], inputs[1])   // Carry bit
      };
    }
  };
  
  // Create FULL_ADDER
  public static MultiGate FULL_ADDER = new MultiGate() {
    public boolean[] eval(boolean... inputs)
    {
      if (inputs.length != 3)
        throw new IllegalArgumentException();
      // Inputs: CarryIn, A, B
      // Outputs: S, CarryOut
      boolean[] haOutputs1 = HALF_ADDER.eval(inputs[0], inputs[1]);
      boolean[] haOutputs2 = HALF_ADDER.eval(haOutputs1[0], inputs[2]);
      return new boolean[] {
        haOutputs2[0],                         // Output bit
        OR.eval(haOutputs1[1], haOutputs2[1])  // Carry bit
      };
    }
  };
  
  public static MultiGate buildAdder(final int numBits)
  {
    return new MultiGate() {
      public boolean[] eval(boolean... inputs)
      {
        // Inputs: A0, A1, A2..., B0, B1, B2...
        if (inputs.length != (numBits << 1))
          throw new IllegalArgumentException();
        boolean[] outputs = new boolean[numBits + 1];
        boolean[] faInputs = new boolean[3];
        boolean[] faOutputs = null;
        for (int i = 0; i < numBits; i++)
        {
          faInputs[0] = (faOutputs == null) ? false : faOutputs[1];  // CarryIn
          faInputs[1] = inputs[i];                                   // Ai
          faInputs[2] = inputs[numBits + i];                         // Bi
          faOutputs = FULL_ADDER.eval(faInputs);
          outputs[i] = faOutputs[0];                                 // Si
        }
        if (faOutputs != null)
          outputs[numBits] = faOutputs[1];                           // CarryOut
        return outputs;
      }
    };
  }
  
  public static void main(String[] args)
  {
    int numBits = Integer.parseInt(args[0]);
    int firstNum = Integer.parseInt(args[1]);
    int secondNum = Integer.parseInt(args[2]);
    int maxNum = 1 << numBits;
    if ((firstNum < 0) || (firstNum >= maxNum))
    {
      System.out.println("First number is out of range");
      return;
    }
    if ((secondNum < 0) || (secondNum >= maxNum))
    {
      System.out.println("Second number is out of range");
      return;
    }
    
    MultiGate multiBitAdder = buildAdder(numBits);
    // Convert input numbers into array of bits
    boolean[] inputs = new boolean[numBits << 1];
    String firstNumDisplay = "";
    String secondNumDisplay = "";
    for (int i = 0; i < numBits; i++)
    {
      boolean firstBit = ((firstNum >>> i) & 1) == 1;
      boolean secondBit = ((secondNum >>> i) & 1) == 1;
      inputs[i] = firstBit;
      inputs[numBits + i] = secondBit;
      firstNumDisplay = (firstBit ? "1" : "0") + firstNumDisplay;
      secondNumDisplay = (secondBit ? "1" : "0") + secondNumDisplay;
    }
    
    boolean[] outputs = multiBitAdder.eval(inputs);
    int outputNum = 0;
    String outputNumDisplay = "";
    String outputCarryDisplay = null;
    for (int i = numBits; i >= 0; i--)
    {
      outputNum = (outputNum << 1) | (outputs[i] ? 1 : 0);
      if (i == numBits)
        outputCarryDisplay = outputs[i] ? "1" : "0";
      else
        outputNumDisplay += (outputs[i] ? "1" : "0");
    }
    System.out.println("numBits=" + numBits);
    System.out.println("A=" + firstNumDisplay + " (" + firstNum + "), B=" + secondNumDisplay + " (" + secondNum + "), S=" + outputCarryDisplay + " " + outputNumDisplay + " (" + outputNum + ")");
    return;
  }
  
}
Output:
java GateLogic 4 9 5
numBits=4
A=1001 (9), B=0101 (5), S=0 1110 (14)

java GateLogic 16 51239 15210
numBits=16
A=1100100000100111 (51239), B=0011101101101010 (15210), S=1 0000001110010001 (66449)

JavaScript

Error Handling

In order to keep the binary-ness obvious, all operations will occur on 0s and 1s. To enforce this, we'll first create a couple of helper functions.

function acceptedBinFormat(bin) {
    if (bin == 1 || bin === 0 || bin === '0')
        return true;
    else
        return bin;
}

function arePseudoBin() {
    var args = [].slice.call(arguments), len = args.length;
    while(len--)
        if (acceptedBinFormat(args[len]) !== true)
            throw new Error('argument must be 0, \'0\', 1, or \'1\', argument ' + len + ' was ' + args[len]);
    return true;
}

Implementation

Now we build up the gates, starting with 'not' and 'and' as building blocks. Those allow us to construct 'nand', 'or', and 'xor' then a half and full adders and, finally, the four bit adder.

// basic building blocks allowed by the rules are ~, &, and |, we'll fake these
// in a way that makes what they do (at least when you use them) more obvious 
// than the other available options do.

function not(a) {
    if (arePseudoBin(a))
        return a == 1 ? 0 : 1;
}

function and(a, b) {
    if (arePseudoBin(a, b))
        return a + b < 2 ? 0 : 1;
}

function nand(a, b) {
    if (arePseudoBin(a, b))
        return not(and(a, b));
}

function or(a, b) {
    if (arePseudoBin(a, b))
        return nand(nand(a,a), nand(b,b));
}

function xor(a, b) {
    if (arePseudoBin(a, b))
        return nand(nand(nand(a,b), a), nand(nand(a,b), b));
}

function halfAdder(a, b) {
    if (arePseudoBin(a, b))
        return { carry: and(a, b), sum: xor(a, b) };
}

function fullAdder(a, b, c) {
    if (arePseudoBin(a, b, c)) {
        var h0 = halfAdder(a, b), 
            h1 = halfAdder(h0.sum, c);
        return {carry: or(h0.carry, h1.carry), sum: h1.sum };
    }
}

function fourBitAdder(a, b) {
    if (typeof a.length == 'undefined' || typeof b.length == 'undefined')
        throw new Error('bad values');
    // not sure if the rules allow this, but we need to pad the values 
    // if they're too short and trim them if they're too long
    var inA = Array(4), 
        inB = Array(4), 
        out = Array(4), 
        i = 4, 
        pass;
    
    while (i--) {
        inA[i] = a[i] != 1 ? 0 : 1;
        inB[i] = b[i] != 1 ? 0 : 1;
    }

    // now we can start adding... I'd prefer to do this in a loop, 
    // but that wouldn't be "connecting the other 'constructive blocks', 
    // in turn made of 'simpler' and 'smaller' ones"
    
    pass = halfAdder(inA[3], inB[3]);
    out[3] = pass.sum;
    pass = fullAdder(inA[2], inB[2], pass.carry);
    out[2] = pass.sum;
    pass = fullAdder(inA[1], inB[1], pass.carry);
    out[1] = pass.sum;
    pass = fullAdder(inA[0], inB[0], pass.carry);
    out[0] = pass.sum;
    return out.join('');
}

Example Use

fourBitAdder('1010', '0101'); // 1111 (15)

all results:

// run this in your browsers console
var outer = inner = 16, a, b;

while(outer--) {
    a = (8|outer).toString(2);
    while(inner--) {
        b = (8|inner).toString(2);
        console.log(a + ' + ' + b + ' = ' + fourBitAdder(a, b));
    }
    inner = outer;
}

jq

Adaptation of the JavaScript entry, but without most of the honesty checks.

All the operations except fourBitAdder(a,b) assume the inputs are presented as 0 or 1 (i.e. integers).

# Start with the 'not' and 'and' building blocks.
# These allow us to construct 'nand', 'or', and 'xor',
# and so on.

def bit_not: if . == 1 then 0 else 1 end;

def bit_and(a; b): if a == 1 and b == 1 then 1 else 0 end;

def bit_nand(a; b): bit_and(a; b) | bit_not;

def bit_or(a; b): bit_nand(bit_nand(a;a); bit_nand(b;b));

def bit_xor(a; b):
  bit_nand(bit_nand(bit_nand(a;b); a); 
           bit_nand(bit_nand(a;b); b));

def halfAdder(a; b): 
  { "carry": bit_and(a; b), "sum": bit_xor(a; b) };

def fullAdder(a; b; c):
  halfAdder(a; b) as $h0 
  | halfAdder($h0.sum; c) as $h1
  | {"carry": bit_or($h0.carry; $h1.carry), "sum": $h1.sum };

# a and b should be strings of 0s and 1s, of length no greater than 4
def fourBitAdder(a; b):

  # pad on the left with 0s, and convert the string
  # representation ("101") to an array of integers ([1,0,1]).
  def pad: (4-length) * "0" + . | explode | map(. - 48);
  
  (a|pad) as $inA | (b|pad) as $inB
  | [][3] = null                                # an array for storing the four results
  | halfAdder($inA[3]; $inB[3]) as $pass
  | .[3] = $pass.sum                            # store the lsb
  | fullAdder($inA[2]; $inB[2]; $pass.carry) as $pass
  | .[2] = $pass.sum
  | fullAdder($inA[1]; $inB[1]; $pass.carry) as $pass
  | .[1] = $pass.sum
  | fullAdder($inA[0]; $inB[0]; $pass.carry) as $pass 
  | .[0] = $pass.sum
  | map(tostring) | join("") ;

Example:

fourBitAdder("0111"; "0001")
Output:
$ jq -n -f Four_bit_adder.jq
"1000"

Jsish

Based on Javascript entry.

#!/usr/bin/env jsish
/* 4 bit adder simulation, in Jsish */
function not(a) { return a == 1 ? 0 : 1; }
function and(a, b) { return a + b < 2 ? 0 : 1; }
function nand(a, b) { return not(and(a, b)); }
function or(a, b) { return nand(nand(a,a), nand(b,b)); }
function xor(a, b) { return nand(nand(nand(a,b), a), nand(nand(a,b), b)); }

function halfAdder(a, b) { return { carry: and(a, b), sum: xor(a, b) }; }
function fullAdder(a, b, c) {
    var h0 = halfAdder(a, b), 
        h1 = halfAdder(h0.sum, c);
    return {carry: or(h0.carry, h1.carry), sum: h1.sum };
}
 
function fourBitAdder(a, b) {
    // set to width 4, pad with 0 if too short and truncate right if too long
    var inA = Array(4), 
        inB = Array(4), 
        out = Array(4), 
        i = 4, 
        pass;
 
    if (a.length < 4) a = '0'.repeat(4 - a.length) + a;
    a = a.slice(-4);
    if (b.length < 4) b = '0'.repeat(4 - b.length) + b;
    b = b.slice(-4);
    while (i--) {
        var re = /0|1/;
        if (a[i] && !re.test(a[i])) throw('bad bit at a[' + i + '] of ' + quote(a[i]));
        if (b[i] && !re.test(b[i])) throw('bad bit at b[' + i + '] of ' + quote(b[i]));
        inA[i] = a[i] != 1 ? 0 : 1;
        inB[i] = b[i] != 1 ? 0 : 1;
    }

    printf('%s + %s = ', a, b);
 
    // now we can start adding... connecting the constructive blocks
    pass = halfAdder(inA[3], inB[3]);
    out[3] = pass.sum;
    pass = fullAdder(inA[2], inB[2], pass.carry);
    out[2] = pass.sum;
    pass = fullAdder(inA[1], inB[1], pass.carry);
    out[1] = pass.sum;
    pass = fullAdder(inA[0], inB[0], pass.carry);
    out[0] = pass.sum;

    var result = parseInt(pass.carry + out.join(''), 2);
    printf('%s  %d\n', out.join('') + ' carry ' + pass.carry, result);
    return result;
}

if (Interp.conf('unitTest')) {
    var bits = [['0000', '0000'], ['0000', '0001'], ['1000', '0001'],
                ['1010', '0101'], ['1000', '1000'], ['1100', '1100'],
                ['1111', '1111']];
    for (var pair of bits) {
        fourBitAdder(pair[0], pair[1]);
    }
;   fourBitAdder('1', '11');
;   fourBitAdder('10001', '01110');
;// fourBitAdder('0002', 'b');
}

/*
=!EXPECTSTART!=
0000 + 0000 = 0000 carry 0  0
0000 + 0001 = 0001 carry 0  1
1000 + 0001 = 1001 carry 0  9
1010 + 0101 = 1111 carry 0  15
1000 + 1000 = 0000 carry 1  16
1100 + 1100 = 1000 carry 1  24
1111 + 1111 = 1110 carry 1  30
fourBitAdder('1', '11') ==> 0001 + 0011 = 0100 carry 0  4
4
fourBitAdder('10001', '01110') ==> 0001 + 1110 = 1111 carry 0  15
15
fourBitAdder('0002', 'b') ==>
PASS!: err = bad bit at a[3] of "2"
=!EXPECTEND!=
*/
Output:
prompt$ jsish --U fourBitAdder.jsi
0000 + 0000 = 0000 carry 0  0
0000 + 0001 = 0001 carry 0  1
1000 + 0001 = 1001 carry 0  9
1010 + 0101 = 1111 carry 0  15
1000 + 1000 = 0000 carry 1  16
1100 + 1100 = 1000 carry 1  24
1111 + 1111 = 1110 carry 1  30
fourBitAdder('1', '11') ==> 0001 + 0011 = 0100 carry 0  4
4
fourBitAdder('10001', '01110') ==> 0001 + 1110 = 1111 carry 0  15
15
fourBitAdder('0002', 'b') ==>
PASS!: err = bad bit at a[3] of "2"

prompt$ jsish -u fourBitAdder.jsi
[PASS] fourBitAdder.jsi

Julia

This solution implements xor, halfadder and fulladder with type Bool. adder is implemented for addends of type BitArray, which can be or arbitrary length (though if a and b have unequal lengths it throws an error). A helper version of adder converts integer inputs to BitArray prior to calling the base version of this function. The length of the BitArrays used in this conversion is adjustable, but in the spirit of this task, it has a default of 4.

Functions

using Printf

xor{T<:Bool}(a::T, b::T) = (a&~b)|(~a&b)

halfadder{T<:Bool}(a::T, b::T) = (xor(a,b), a&b)

function fulladder{T<:Bool}(a::T, b::T, c::T=false)
    (s, ca) = halfadder(c, a)
    (s, cb) = halfadder(s, b)
    (s, ca|cb)
end

function adder(a::BitArray{1}, b::BitArray{1}, c0::Bool=false)
    len = length(a)
    length(b) == len || error("Addend width mismatch.")
    c = c0
    s = falses(len)
    for i in 1:len
        (s[i], c) = fulladder(a[i], b[i], c)
    end
    (s, c)
end

function adder{T<:Integer}(m::T, n::T, wid::T=4, c0::Bool=false)
    a = bitpack(digits(m, 2, wid))[1:wid]
    b = bitpack(digits(n, 2, wid))[1:wid]
    adder(a, b, c0)
end

Base.bits(n::BitArray{1}) = join(reverse(int(n)), "")

Main

xavail = trues(15,15)
xcnt = 0
xgoal = 10
println("Testing adder with 4-bit words:")
while xcnt < xgoal
    m = rand(1:15)
    n = rand(1:15)
    xavail[m,n] || continue
    xavail[m,n] = xavail[n,m] = false
    xcnt += 1
    (s, c) = adder(m, n)
    oflow = c ? "*" : ""
    print(@sprintf "    %2d + %2d = %2d => " m n m+n)
    println(@sprintf("%s + %s = %s%s",
                     bits(m)[end-3:end],
                     bits(n)[end-3:end],
                     bits(s), oflow))
end
Output:
Testing adder with 4-bit words:
     6 + 14 = 20 => 0110 + 1110 = 0100*
     5 +  6 = 11 => 0101 + 0110 = 1011
     5 +  3 =  8 => 0101 + 0011 = 1000
     1 +  7 =  8 => 0001 + 0111 = 1000
    15 +  6 = 21 => 1111 + 0110 = 0101*
     1 + 14 = 15 => 0001 + 1110 = 1111
     8 +  9 = 17 => 1000 + 1001 = 0001*
    14 + 10 = 24 => 1110 + 1010 = 1000*
     3 +  1 =  4 => 0011 + 0001 = 0100
     6 + 11 = 17 => 0110 + 1011 = 0001*

Kotlin

// version 1.1.51

val Boolean.I get() = if (this) 1 else 0

val Int.B get() = this != 0

class Nybble(val n3: Boolean, val n2: Boolean, val n1: Boolean, val n0: Boolean) {
    fun toInt() = n0.I + n1.I * 2 + n2.I * 4 + n3.I * 8

    override fun toString() = "${n3.I}${n2.I}${n1.I}${n0.I}"
}

fun Int.toNybble(): Nybble {
    val n = BooleanArray(4)
    for (k in 0..3) n[k] = ((this shr k) and 1).B
    return Nybble(n[3], n[2], n[1], n[0])
}

fun xorGate(a: Boolean, b: Boolean) = (a && !b) || (!a && b)

fun halfAdder(a: Boolean, b: Boolean) = Pair(xorGate(a, b), a && b)

fun fullAdder(a: Boolean, b: Boolean, c: Boolean): Pair<Boolean, Boolean> {
    val (s1, c1) = halfAdder(c, a)
    val (s2, c2) = halfAdder(s1, b)
    return s2 to (c1 || c2)
}

fun fourBitAdder(a: Nybble, b: Nybble): Pair<Nybble, Int> {
    val (s0, c0) = fullAdder(a.n0, b.n0, false)
    val (s1, c1) = fullAdder(a.n1, b.n1, c0)
    val (s2, c2) = fullAdder(a.n2, b.n2, c1)
    val (s3, c3) = fullAdder(a.n3, b.n3, c2)
    return Nybble(s3, s2, s1, s0) to c3.I
}

const val f = "%s + %s = %d %s (%2d + %2d = %2d)"

fun test(i: Int, j: Int) {
    val a = i.toNybble()
    val b = j.toNybble()
    val (r, c) = fourBitAdder(a, b)
    val s = c * 16 + r.toInt()
    println(f.format(a, b, c, r, i, j, s))
}

fun main(args: Array<String>) {
    println(" A      B     C  R     I    J    S")
    for (i in 0..15) {
        for (j in i..minOf(i + 1, 15)) test(i, j)
    }
}
Output:
 A      B     C  R     I    J    S
0000 + 0000 = 0 0000 ( 0 +  0 =  0)
0000 + 0001 = 0 0001 ( 0 +  1 =  1)
0001 + 0001 = 0 0010 ( 1 +  1 =  2)
0001 + 0010 = 0 0011 ( 1 +  2 =  3)
0010 + 0010 = 0 0100 ( 2 +  2 =  4)
0010 + 0011 = 0 0101 ( 2 +  3 =  5)
0011 + 0011 = 0 0110 ( 3 +  3 =  6)
0011 + 0100 = 0 0111 ( 3 +  4 =  7)
0100 + 0100 = 0 1000 ( 4 +  4 =  8)
0100 + 0101 = 0 1001 ( 4 +  5 =  9)
0101 + 0101 = 0 1010 ( 5 +  5 = 10)
0101 + 0110 = 0 1011 ( 5 +  6 = 11)
0110 + 0110 = 0 1100 ( 6 +  6 = 12)
0110 + 0111 = 0 1101 ( 6 +  7 = 13)
0111 + 0111 = 0 1110 ( 7 +  7 = 14)
0111 + 1000 = 0 1111 ( 7 +  8 = 15)
1000 + 1000 = 1 0000 ( 8 +  8 = 16)
1000 + 1001 = 1 0001 ( 8 +  9 = 17)
1001 + 1001 = 1 0010 ( 9 +  9 = 18)
1001 + 1010 = 1 0011 ( 9 + 10 = 19)
1010 + 1010 = 1 0100 (10 + 10 = 20)
1010 + 1011 = 1 0101 (10 + 11 = 21)
1011 + 1011 = 1 0110 (11 + 11 = 22)
1011 + 1100 = 1 0111 (11 + 12 = 23)
1100 + 1100 = 1 1000 (12 + 12 = 24)
1100 + 1101 = 1 1001 (12 + 13 = 25)
1101 + 1101 = 1 1010 (13 + 13 = 26)
1101 + 1110 = 1 1011 (13 + 14 = 27)
1110 + 1110 = 1 1100 (14 + 14 = 28)
1110 + 1111 = 1 1101 (14 + 15 = 29)
1111 + 1111 = 1 1110 (15 + 15 = 30)

LabVIEW

LabVIEW's G language is a kind of circuit diagram based programming. Thus, a circuit diagram is pseudo-code for a G block diagram, which makes coding a four bit adder trivial.

Works with: LabVIEW version 8.0 Full Development Suite



Half Adder

    

Full Adder

    

4bit Adder

    

Lambdatalk

{def xor
 {lambda {:a :b} 
  {or {and :a {not :b}} {and :b {not :a}}}}}
-> xor

{def halfAdder
 {lambda {:a :b}
  {cons {and :a :b} {xor :a :b}}}}
-> halfAdder

{def fullAdder 
 {lambda {:a :b :c}
  {let {  {:b :b}
          {:ha1 {halfAdder :c :a}} }
   {let { {:ha1 :ha1}
          {:ha2 {halfAdder {cdr :ha1} :b}} }
        {cons {or {car :ha1} {car :ha2}} {cdr :ha2}} }}}}
-> fullAdder

{def 4bitsAdder
 {lambda {:a4 :a3 :a2 :a1 :b4 :b3 :b2 :b1}
  {let { {:a4 :a4} {:a3 :a3} {:a2 :a2} {:b4 :b4} {:b3 :b3} {:b2 :b2}
         {:fa1 {fullAdder :a1 :b1 false}} }
   {let { {:a4 :a4} {:a3 :a3} {:b4 :b4} {:b3 :b3}
          {:fa1 :fa1} 
          {:fa2 {fullAdder :a2 :b2 {car :fa1}}} }
    {let { {:a4 :a4} {:b4 :b4}
           {:fa1 :fa1} {:fa2 :fa2} 
           {:fa3 {fullAdder :a3 :b3 {car :fa2}}} }
     {let { {:fa1 :fa1} {:fa2 :fa2} {:fa3 :fa3}
            {:fa4 {fullAdder :a4 :b4 {car :fa3}}} }
      {car :fa4} {cdr :fa4} {cdr :fa3} {cdr :fa2} {cdr :fa1}}}}}}}
-> 4bitsAdder

{def bin2bool 
 {lambda {:b}
  {if {W.empty? {W.rest :b}}
   then {= {W.first :b} 1}
   else {= {W.first :b} 1} {bin2bool {W.rest :b}}}}}
-> bin2bool

{def bool2bin
 {lambda {:b}
  {if {S.empty? {S.rest :b}}
   then {if {S.first :b} then 1 else 0} 
   else {if {S.first :b} then 1 else 0}{bool2bin {S.rest :b}}}}}
-> bool2bin

{def bin2dec
 {def bin2dec.r
  {lambda {:p :r}
   {if {A.empty? :p}
    then :r
    else {bin2dec.r {A.rest :p} {+ {A.first :p} {* 2 :r}}}}}}
 {lambda {:p} {bin2dec.r {A.split :p} 0}}}
-> bin2dec

{def add
 {def numbers 0000 0001 0010 0011 0100 0101 0110 0111
              1000 1001 1010 1011 1100 1101 1110 1111}
 {lambda {:a :b}
  {bin2dec
   {bool2bin
    {4bitsAdder {bin2bool {S.get :a {numbers}}}
                {bin2bool {S.get :b {numbers}}}}}}}}
-> add

{table
 {S.map {lambda {:i} {tr
  {S.map {{lambda {:i :j} {td {add :i :j}}} :i}  
  {S.serie 0 15}}}} 
 {S.serie 0 15}}
}
-> 
 0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15
 1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16
 2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17
 3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18
 4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19
 5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20
 6   7   8   9  10  11  12  13  14  15  16  17  18  19  20  21
 7   8   9  10  11  12  13  14  15  16  17  18  19  20  21  22
 8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23
 9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24
10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25
11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26
12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27
13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28
14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29
15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30

Lua

-- Build XOR from AND, OR and NOT
function xor (a, b) return (a and not b) or (b and not a) end
 
-- Can make half adder now XOR exists
function halfAdder (a, b) return xor(a, b), a and b end
 
-- Full adder is two half adders with carry outputs OR'd
function fullAdder (a, b, cIn)
    local ha0s, ha0c = halfAdder(cIn, a)
    local ha1s, ha1c = halfAdder(ha0s, b)
    local cOut, s = ha0c or ha1c, ha1s
    return cOut, s
end
 
-- Carry bits 'ripple' through adders, first returned value is overflow
function fourBitAdder (a3, a2, a1, a0, b3, b2, b1, b0) -- LSB-first
    local fa0c, fa0s = fullAdder(a0, b0, false)
    local fa1c, fa1s = fullAdder(a1, b1, fa0c)
    local fa2c, fa2s = fullAdder(a2, b2, fa1c)
    local fa3c, fa3s = fullAdder(a3, b3, fa2c)
    return fa3c, fa3s, fa2s, fa1s, fa0s -- Return as MSB-first
end
 
-- Take string of noughts and ones, convert to native boolean type
function toBool (bitString)
    local boolList, bit = {}
    for digit = 1, 4 do
        bit = string.sub(string.format("%04d", bitString), digit, digit)
        if bit == "0" then table.insert(boolList, false) end
        if bit == "1" then table.insert(boolList, true) end
    end
    return boolList
end
 
-- Take list of booleans, convert to string of binary digits (variadic)
function toBits (...)
    local bStr = ""
    for i, bool in pairs{...} do
        if bool then bStr = bStr .. "1" else bStr = bStr .. "0" end
    end
    return bStr
end
 
-- Little driver function to neaten use of the adder
function add (n1, n2)
    local A, B = toBool(n1), toBool(n2)
    local v, s0, s1, s2, s3 = fourBitAdder( A[1], A[2], A[3], A[4],
                                            B[1], B[2], B[3], B[4] )
    return toBits(s0, s1, s2, s3), v
end
 
-- Main procedure (usage examples)
print("SUM", "OVERFLOW\n")
print(add(0001, 0001)) -- 1 + 1 = 2
print(add(0101, 1010)) -- 5 + 10 = 15
print(add(0000, 1111)) -- 0 + 15 = 15
print(add(0001, 1111)) -- 1 + 15 = 16 (causes overflow)

Output:

SUM     OVERFLOW

0010    false
1111    false
1111    false
0000    true

M2000 Interpreter

Module  FourBitAdder {
	Flush
	dim not(0 to 1),and(0 to 1, 0 to 1),or(0 to 1, 0 to 1)
	not(0)=1,0
	and(0,0)=0,0,0,1
	or(0,0)=0,1,1,1
	xor=lambda not(),and(),or() (a,b)-> or(and(a, not(b)), and(b, not(a)))
	ha=lambda xor, and() (a,b, &s, &c)->{
		s=xor(a,b)
		c=and(a,b)
	}
	fa=lambda ha, or() (a, b, c0, &s, &c1)->{
		def sa,ca,cb
		call ha(a, c0, &sa, &ca)
		call ha(sa, b, &s,&cb)
		c1=or(ca,cb)
	}
	add4=lambda fa (inpA(), inpB(), &v, &out()) ->{
		dim carry(0 to 4)=0
		carry(0)=v    \\ 0 or 1  borrow
		for i=0 to 3
			\\ mm=fa(InpA(i), inpB(i), carry(i), &out(i), &carry(i+1)) ' same as this
			Call fa(InpA(i), inpB(i), carry(i), &out(i), &carry(i+1))
		next
		v=carry(4)
	}
	dim res(0 to 3)=-1,  low()
	source=lambda->{
		shift 1, -stack.size  ' reverse stack items
		=array([])  ' convert current stack to array, empty current stack
	}
	def v, k, k_low
	Print "First Example 4-bit"
	Print "A", "", 1, 0, 1, 0
	Print "B", "", 1, 0, 0, 1
	call add4(source(1,0,1,0), source(1,0,0,1), &v, &res())
	k=each(res() end to start)  ' k is an iterator, now configure to read items in reverse
	Print "A+B",v, k    ' print 1 0 0 1 1
	Print "Second Example 4-bit"
	v-=v
	Print "A", "", 0, 1, 1, 0
	Print "B", "", 0, 1, 1, 1
	call add4(source(0,1,1,0), source(0,1,1,1), &v, &res())
	k=each(res() end to start)  ' k is an iterator, now configure to read items in reverse
	Print "A+B",v, k    ' print  0 1 1 0 1
	Print "Third Example 8-bit"
	v-=v
	Print "A ", "", 1, 0, 0, 0, 0, 1, 1, 0
	Print "B ", "", 1, 1, 1, 1, 1, 1, 1, 1
	call add4(source(0,1,1,0), source(1,1,1,1), &v, &res())
	low()=res()  ' a copy of res()
	' v passed to second adder
	dim res(0 to 3)=-1
	call add4(source(1,0,0,0), source(1,1,1,1), &v, &res())
	k_low=each(low() end to start)  ' k_low is an iterator, now configure to read items in reverse
	k=each(res() end to start)  ' k is an iterator, now configure to read items in reverse
	Print "A+B",v, k, k_low   ' print  1 1 0 0 0 0 1 0 1
}
FourBitAdder

Mathematica / Wolfram Language

and[a_, b_] := Max[a, b];
or[a_, b_] := Min[a, b];
not[a_] := 1 - a;
xor[a_, b_] := or[and[a, not[b]], and[b, not[a]]];
halfadder[a_, b_] := {xor[a, b], and[a, b]};
fulladder[a_, b_, c0_] := Module[{s, c, c1},
   {s, c} = halfadder[c0, a];
   {s, c1} = halfadder[s, b];
   {s, or[c, c1]}];
fourbitadder[{a3_, a2_, a1_, a0_}, {b3_, b2_, b1_, b0_}] := 
  Module[{s0, s1, s2, s3, c0, c1, c2, c3},
   {s0, c0} = fulladder[a0, b0, 0];
   {s1, c1} = fulladder[a1, b1, c0];
   {s2, c2} = fulladder[a2, b2, c1];
   {s3, c3} = fulladder[a3, b3, c2];
   {{s3, s2, s1, s0}, c3}];

Example:

fourbitadder[{1, 0, 1, 0}, {1, 1, 1, 1}]

Output:

{{1, 0, 0, 1}, 1}

MATLAB / Octave

The four bit adder presented can work on matricies of 1's and 0's, which are stored as characters, doubles, or booleans. MATLAB has functions to convert decimal numbers to binary, but these functions convert a decimal number not to binary but a string data type of 1's and 0's. So, this four bit adder is written to be compatible with MATLAB's representation of binary. Also, because this is MATLAB, and you might want to add arrays of 4-bit binary numbers together, this implementation will add two column vectors of 4-bit binary numbers together.

function [S,v] = fourBitAdder(input1,input2)

    %Make sure that only 4-Bit numbers are being added. This assumes that
    %if input1 and input2 are a vector of multiple decimal numbers, then
    %the binary form of these vectors are an n by 4 matrix.
    assert((size(input1,2) == 4) && (size(input2,2) == 4),'This will only work on 4-Bit Numbers');
    
    %Converts MATLAB binary strings to matricies of 1 and 0
    function mat = binStr2Mat(binStr)
        mat = zeros(size(binStr));      
        for i = (1:numel(binStr))
            mat(i) = str2double(binStr(i));
        end
    end
    
    %XOR decleration
    function AxorB = xor(A,B)        
        AxorB = or(and(A,not(B)),and(B,not(A)));    
    end

    %Half-Adder decleration
    function [S,C] = halfAdder(A,B)
        S = xor(A,B);
        C = and(A,B);
    end

    %Full-Adder decleration
    function [S,Co] = fullAdder(A,B,Ci)
       [SAdder1,CAdder1] = halfAdder(Ci,A);
       [S,CAdder2] = halfAdder(SAdder1,B);
       Co = or(CAdder1,CAdder2);
    end

    %The rest of this code is the 4-bit adder
    
    binStrFlag = false; %A flag to determine if the original input was a binary string
    
    %If either of the inputs was a binary string, convert it to a matrix of
    %1's and 0's.
    if ischar(input1)
       input1 = binStr2Mat(input1);
       binStrFlag = true;
    end
    if ischar(input2)
       input2 = binStr2Mat(input2);
       binStrFlag = true;
    end

    %This does the addition
    S = zeros(size(input1));

    [S(:,4),Co] = fullAdder(input1(:,4),input2(:,4),0);
    [S(:,3),Co] = fullAdder(input1(:,3),input2(:,3),Co);
    [S(:,2),Co] = fullAdder(input1(:,2),input2(:,2),Co);
    [S(:,1),v] = fullAdder(input1(:,1),input2(:,1),Co);
    
    %If the original inputs were binary strings, convert the output of the
    %4-bit adder to a binary string with the same formatting as the
    %original binary strings.
    if binStrFlag
        S = num2str(S);
        v = num2str(v);
    end
end %fourBitAdder

Sample Usage:

>> [S,V] = fourBitAdder([0 0 0 1],[1 1 1 1])

S =

     0     0     0     0


V =

     1

>> [S,V] = fourBitAdder([0 0 0 1;0 0 1 0],[0 0 0 1;0 0 0 1])

S =

     0     0     1     0
     0     0     1     1


V =

     0
     0

>> [S,V] = fourBitAdder(dec2bin(10,4),dec2bin(1,4))

S =

1  0  1  1


V =

0

>> [S,V] = fourBitAdder(dec2bin([10 11],4),dec2bin([1 1],4))

S =

1  0  1  1
1  1  0  0


V =

0
0

>> bin2dec(S)

ans =

    11
    12

MUMPS

XOR(Y,Z) ;Uses logicals - i.e., 0 is false, anything else is true (1 is used if setting a value)
 QUIT (Y&'Z)!('Y&Z)
HALF(W,X)
 QUIT $$XOR(W,X)_"^"_(W&X)
FULL(U,V,CF)
 NEW F1,F2
 S F1=$$HALF(U,V)
 S F2=$$HALF($P(F1,"^",1),CF)
 QUIT $P(F2,"^",1)_"^"_($P(F1,"^",2)!($P(F2,"^",2)))
FOUR(Y,Z,C4)
 NEW S,I,T
 FOR I=4:-1:1 SET T=$$FULL($E(Y,I),$E(Z,I),C4),$E(S,I)=$P(T,"^",1),C4=$P(T,"^",2)
 K I,T
 QUIT S_"^"_C4

Usage:

USER>S N1="0110",N2="0010",C=0,T=$$FOUR^ADDER(N1,N2,C)
 
USER>W N1_" + "_N2_" + "_C_" = "_$P(T,"^")_" Carry "_$P(T,"^",2)
0110 + 0010 + 0 = 1000 Carry 0
USER>S N1="0110",N2="1110",C=0,T=$$FOUR^ADDER(N1,N2,C)
 
USER>W T
0100^1
USER>W N1_" + "_N2_" + "_C_" = "_$P(T,"^")_" Carry "_$P(T,"^",2)
0110 + 1110 + 0 = 0100 Carry 1

MyHDL

To interpret and run this code you will need a copy of Python3, and the MyHDL library from myhdl.org (pip3 install myhdl).

The test code simulates the adder and exports trace wave file for debug support. Verilog and VHDL files are exported for hardware synthesis.

"""  
To run: 
    python3 Four_bit_adder_011.py
"""

from myhdl import *

#     define set of primitives 

@block
def NOTgate( a,  q ):   # define component name & interface
   """ q <- not(a) """
   @always_comb   # define asynchronous logic
   def NOTgateLogic():
      q.next = not a

   return NOTgateLogic   # return defined logic function, named 'NOTgate'


@block
def ANDgate( a, b,  q ):
   """ q <- a and b """
   @always_comb 
   def ANDgateLogic():
      q.next = a and b

   return ANDgateLogic


@block
def ORgate( a, b,  q ):
   """ q <- a or b """   
   @always_comb  
   def ORgateLogic():
      q.next = a or b

   return ORgateLogic


#     build components using defined primitive set

@block
def XORgate( a, b,  q ):
   """ q <- a xor b """   
   # define internal signals
   nota, notb, annotb, bnnota = [Signal(bool(0)) for i in range(4)]
   # name sub-components, and their interconnect 
   inv0 = NOTgate( a,  nota )
   inv1 = NOTgate( b,  notb )
   and2a = ANDgate( a, notb,  annotb )
   and2b = ANDgate( b, nota,  bnnota )
   or2a = ORgate( annotb, bnnota,  q )

   return inv0, inv1, and2a, and2b, or2a


@block
def HalfAdder( in_a, in_b,  summ, carry ):
   """ carry,sum is the sum of in_a, in_b """ 
   and2a =  ANDgate(in_a, in_b,  carry)
   xor2a =  XORgate(in_a, in_b,  summ)

   return and2a, xor2a


@block
def FullAdder( fa_c0, fa_a, fa_b,  fa_s, fa_c1 ):
   """ fa_c1,fa_s is the sum of fa_c0, fa_a, fa_b """

   ha1_s, ha1_c1, ha2_c1 = [Signal(bool(0)) for i in range(3)]

   HalfAdder01 = HalfAdder( fa_c0, fa_a,  ha1_s, ha1_c1 )
   HalfAdder02 = HalfAdder( ha1_s, fa_b,  fa_s,  ha2_c1 )
   or2a = ORgate(ha1_c1, ha2_c1,  fa_c1)

   return HalfAdder01, HalfAdder02, or2a


@block
def Adder4b( ina, inb,  cOut, sum4):
   ''' assemble 4 full adders ''' 

   cl = [Signal(bool()) for i in range(0,4)]  # carry signal list
   sl = [Signal(bool()) for i in range(4)]  # sum signal list

   HalfAdder0 = HalfAdder(        ina(0), inb(0),  sl[0], cl[1] )
   FullAdder1 = FullAdder( cl[1], ina(1), inb(1),  sl[1], cl[2] ) 
   FullAdder2 = FullAdder( cl[2], ina(2), inb(2),  sl[2], cl[3] ) 
   FullAdder3 = FullAdder( cl[3], ina(3), inb(3),  sl[3], cOut ) 

   sc = ConcatSignal(*reversed(sl))  # create internal bus for output list

   @always_comb
   def list2intbv():
      sum4.next = sc  # assign internal bus to actual output

   return HalfAdder0, FullAdder1, FullAdder2, FullAdder3, list2intbv


"""   define signals and code for testing
      -----------------------------------   """
t_co, t_s, t_a, t_b, dbug =  [Signal(bool(0)) for i in range(5)]
ina4, inb4, sum4 =  [Signal(intbv(0)[4:])  for i in range(3)]

from random import randrange 

@block
def Test_Adder4b():
   ''' Test Bench for Adder4b '''
   dut = Adder4b( ina4, inb4,  t_co, sum4 )

   @instance
   def check():
      print( "\n      b   a   |  c1    s   \n     -------------------" )
      for i in range(15):
         ina4.next, inb4.next = randrange(2**4), randrange(2**4)
         yield delay(5)
         print( "     %2d  %2d   |  %2d   %2d     " \
                % (ina4,inb4, t_co,sum4) )
         assert t_co * 16 + sum4 == ina4 + inb4  # test result
      print()

   return dut, check


"""   instantiate components and run test
      -----------------------------------   """

def main():
   simInst = Test_Adder4b()
   simInst.name = "mySimInst"
   simInst.config_sim(trace=True)  # waveform trace turned on
   simInst.run_sim(duration=None)

   inst = Adder4b( ina4, inb4,  t_co, sum4 )  #Multibit_Adder( a, b, s)
   inst.convert(hdl='VHDL')  # export VHDL
   inst.convert(hdl='Verilog')  # export Verilog

    
if __name__ == '__main__':
   main()

Nim

Translation of: Python
type

  Bools[N: static int] = array[N, bool]
  SumCarry = tuple[sum, carry: bool]

proc ha(a, b: bool): SumCarry = (a xor b, a and b)

proc fa(a, b, ci: bool): SumCarry =
  let a = ha(ci, a)
  let b = ha(a[0], b)
  result = (b[0], a[1] or b[1])

proc fa4(a, b: Bools[4]): Bools[5] =
  var co, s: Bools[4]
  for i in 0..3:
    let r = fa(a[i], b[i], if i > 0: co[i-1] else: false)
    s[i] = r[0]
    co[i] = r[1]
  result[0..3] = s
  result[4] = co[3]

proc int2bus(n: int): Bools[4] =
  var n = n
  for i in 0..result.high:
    result[i] = (n and 1) == 1
    n = n shr 1

proc bus2int(b: Bools): int =
  for i, x in b:
    result += (if x: 1 else: 0) shl i

for a in 0..7:
  for b in 0..7:
    assert a + b == bus2int fa4(int2bus(a), int2bus(b))

OCaml

(* File blocks.ml

A block is just a black box with nin input lines and nout output lines,
numbered from 0 to nin-1 and 0 to nout-1 respectively. It will be stored
in a caml record, with the operation stored as a function. A value on
a line is represented by a boolean value. *)

type block = { nin:int; nout:int; apply:bool array -> bool array };;

(* First we need function for boolean conversion to and from integer values,
mainly for pretty printing of results *)

let int_of_bits nbits v =
	if (Array.length v) <> nbits then failwith "bad args"
	else
		(let r = ref 0L in
		for i=nbits-1 downto 0 do
			r := Int64.add (Int64.shift_left !r 1) (if v.(i) then 1L else 0L)
		done;
		!r);;

let bits_of_int nbits n =
	let v = Array.make nbits false
	and r = ref n in
	for i=0 to nbits-1 do
		v.(i) <- (Int64.logand !r 1L) <> Int64.zero;
		r := Int64.shift_right_logical !r 1
	done;
	v;;

let input nbits v =
	let n = Array.length v in
	let w = Array.make (n*nbits) false in
	Array.iteri (fun i x ->
		Array.blit (bits_of_int nbits x) 0 w (i*nbits) nbits
	) v;
	w;;
	
let output nbits v =
	let nv = Array.length v in
	let r = nv mod nbits and n = nv/nbits in
	if r <> 0 then failwith "bad output size" else
	Array.init n (fun i ->
		int_of_bits nbits (Array.sub v (i*nbits) nbits)
	);;

(* We have a type for blocks, so we need operations on blocks.

assoc:        make one block from two blocks, side by side (they are not connected)
serial:       connect input from one block to output of another block
parallel:     make two outputs from one input passing through two blocks
block_array:  an array of blocks linked by the same connector (assoc, serial, parallel) *)

let assoc a b =
	{ nin=a.nin+b.nin; nout=a.nout+b.nout; apply=function
		bits -> Array.append
			(a.apply (Array.sub bits 0 a.nin))
			(b.apply (Array.sub bits a.nin b.nin)) };;

let serial a b =
	if a.nout <> b.nin then
		failwith "[serial] bad block"
	else
	{ nin=a.nin; nout=b.nout; apply=function
		bits -> b.apply (a.apply bits) };;

let parallel a b =
	if a.nin <> b.nin then
		failwith "[parallel] bad blocks"
	else { nin=a.nin; nout=a.nout+b.nout; apply=function
		bits -> Array.append (a.apply bits) (b.apply bits) };;

let block_array comb v =
	let n = Array.length v
	and r = ref v.(0) in
	for i=1 to n-1 do
		r := comb !r v.(i)
	done;
	!r;;

(* wires

map:     map n input lines on length(v) output lines, using the links out(k)=v(in(k))
pass:    n wires not connected (out(k) = in(k))
fork:    a wire is developed into n wires having the same value
perm:    permutation of wires
forget:  n wires going nowhere
sub:     subset of wires, other ones going nowhere *)

let map n v = { nin=n; nout=Array.length v; apply=function
	bits -> Array.map (function k -> bits.(k)) v };;

let pass n = { nin=n; nout=n; apply=function
	bits -> bits };;

let fork n = { nin=1; nout=n; apply=function
	bits -> Array.make n bits.(0) };;

let perm v =
	let n = Array.length v in
	{ nin=n; nout=n; apply=function
		bits -> Array.init n (function k -> bits.(v.(k))) };;
		
let forget n = { nin=n; nout=0; apply=function
	bits -> [| |] };;

let sub nin nout where = { nin=nin; nout=nout; apply=function
	bits -> Array.sub bits where nout };;

let transpose n p v =
	if n*p <> Array.length v
		then failwith "bad dim"
	else
		let w = Array.copy v in
		for i=0 to n-1 do
			for j=0 to p-1 do
				let r = i*p+j and s = j*n+i in
				w.(r) <- v.(s)
			done
		done;
		w;;

(* line mixing (a special permutation)
mix 4 2 : 0,1,2,3, 4,5,6,7 -> 0,4, 1,5, 2,6, 3,7
unmix: inverse operation *)

let mix n p = perm (transpose n p (Array.init (n*p) (function x -> x)));;

let unmix n p = perm (transpose p n (Array.init (n*p) (function x -> x)));;

(* basic blocks

dummy:   no input, no output, usually not useful
const:   n wires with constant value (true or false)
encode:  translates an Int64 into boolean values, keeping only n lower bits
bnand:   NAND gate, the basic building block for all the other basic gates (or, and, not...) *)

let dummy = { nin=0; nout=0; apply=function
	bits -> bits };;

let const b n = { nin=0; nout=n; apply=function
	bits -> Array.make n b };;

let encode nbits x = { nin=0; nout=nbits; apply=function
	bits -> bits_of_int nbits x };;

let bnand = { nin=2; nout=1; apply=function
	[| a; b |] -> [| not (a && b) |] | _ -> failwith "bad args" };;

(* block evaluation : returns the value of the output, given an input and a block. *)

let eval block nbits_in nbits_out v =
	output nbits_out (block.apply (input nbits_in v));;

(* building a 4-bit adder *)

(* first we build the usual gates *)

let bnot = serial (fork 2) bnand;;

let band = serial bnand bnot;;

(* a or b = !a nand !b *)
let bor = serial (assoc bnot bnot) bnand;;

(* line "a" -> two lines, "a" and "not a" *)
let a_not_a = parallel (pass 1) bnot;;

let bxor = block_array serial [|
	assoc a_not_a a_not_a;
	perm [| 0; 3; 1; 2 |];
	assoc band band;
	bor |];;
	
let half_adder = parallel bxor band;;

(* bits C0,A,B -> S,C1 *)
let full_adder = block_array serial [|
	assoc half_adder (pass 1);
	perm [| 1; 0; 2 |];
	assoc (pass 1) half_adder;
	perm [| 1; 0; 2 |];
	assoc (pass 1) bor |];;

(* 4-bit adder *)
let add4 = block_array serial [|
	mix 4 2;
	assoc half_adder (pass 6);
	assoc (assoc (pass 1) full_adder) (pass 4);
	assoc (assoc (pass 2) full_adder) (pass 2);
	assoc (pass 3) full_adder |];;

(* 4-bit adder and three supplementary lines to make a multiple of 4 (to translate back to 4-bit integers) *)
let add4_io = assoc add4 (const false 3);;

(* wrapping the 4-bit to input and output integers instead of booleans
plus a b -> (sum,carry)
*)
let plus a b =
	let v = Array.map Int64.to_int
		(eval add4_io 4 4 (Array.map Int64.of_int [| a; b |])) in
	v.(0), v.(1);;

Testing

# open Blocks;;

# plus 4 5;;
- : int * int = (9, 0)

# plus 15 1;;
- : int * int = (0, 1)

# plus 15 15;;
- : int * int = (14, 1)

# plus 0 0;;
- : int * int = (0, 0)

An extension : n-bit adder, for n <= 64 (n could be greater, but we use Int64 for I/O)

(* general adder (n bits with n <= 64) *)
let gen_adder n = block_array serial [|
	mix n 2;
	assoc half_adder (pass (2*n-2));
	block_array serial (Array.init (n-2) (function k ->
		assoc (assoc (pass (k+1)) full_adder) (pass (2*(n-k-2)))));
	assoc (pass (n-1)) full_adder |];;

let gadd_io n = assoc (gen_adder n) (const false (n-1));;

let gen_plus n a b =
	let v = Array.map Int64.to_int
		(eval (gadd_io n) n n (Array.map Int64.of_int [| a; b |])) in
	v.(0), v.(1);;

And a test

# gen_plus 7 100 100;;
- : int * int = (72, 1)
# gen_plus 8 100 100;;
- : int * int = (200, 0)

PARI/GP

xor(a,b)=(!a&b)||(a&!b);
halfadd(a,b)=[a&&b,xor(a,b)];
fulladd(a,b,c)=my(t=halfadd(a,c),s=halfadd(t[2],b));[t[1]||s[1],s[2]];
add4(a3,a2,a1,a0,b3,b2,b1,b0)={
	my(s0,s1,s2,s3);
	s0=fulladd(a0,b0,0);
	s1=fulladd(a1,b1,s0[1]);
	s2=fulladd(a2,b2,s1[1]);
	s3=fulladd(a3,b3,s2[1]);
	[s3[1],s3[2],s2[2],s1[2],s0[2]]
};
add4(0,0,0,0,0,0,0,0)

Perl

sub dec2bin { sprintf "%04b", shift }
sub bin2dec { oct "0b".shift }
sub bin2bits { reverse split(//, substr(shift,0,shift)); }
sub bits2bin { join "", map { 0+$_ } reverse @_ }

sub bxor {
  my($a, $b) = @_;
  (!$a & $b) | ($a & !$b);
}

sub half_adder {
  my($a, $b) = @_;
  ( bxor($a,$b), $a & $b );
}

sub full_adder {
  my($a, $b, $c) = @_;
  my($s1, $c1) = half_adder($a, $c);
  my($s2, $c2) = half_adder($s1, $b);
  ($s2, $c1 | $c2);
}

sub four_bit_adder {
  my($a, $b) = @_;
  my @abits = bin2bits($a,4);
  my @bbits = bin2bits($b,4);

  my($s0,$c0) = full_adder($abits[0], $bbits[0], 0);
  my($s1,$c1) = full_adder($abits[1], $bbits[1], $c0);
  my($s2,$c2) = full_adder($abits[2], $bbits[2], $c1);
  my($s3,$c3) = full_adder($abits[3], $bbits[3], $c2);
  (bits2bin($s0, $s1, $s2, $s3), $c3);
}

print " A    B      A      B   C    S  sum\n";
for my $a (0 .. 15) {
  for my $b (0 .. 15) {
    my($abin, $bbin) = map { dec2bin($_) } $a,$b;
    my($s,$c) = four_bit_adder( $abin, $bbin );
    printf "%2d + %2d = %s + %s = %s %s = %2d\n",
           $a, $b, $abin, $bbin, $c, $s, bin2dec($c.$s);
  }
}

Output matches the Ruby output.

Phix

with javascript_semantics
function xor_gate(bool a, bool b)
    return (a and not b) or (not a and b)
end function
 
function half_adder(bool a, bool b)
    bool s = xor_gate(a,b),
         c = a and b
    return {s,c}
end function
 
function full_adder(bool a, bool b, bool c)
    bool {s1,c1} = half_adder(c,a),
         {s2,c2} = half_adder(s1,b)
    c = c1 or c2
    return {s2,c}
end function
 
function four_bit_adder(bool a0, a1, a2, a3, b0, b1, b2, b3)
    bool s0,s1,s2,s3,c  
    {s0,c} = full_adder(a0,b0,0)
    {s1,c} = full_adder(a1,b1,c)
    {s2,c} = full_adder(a2,b2,c)
    {s3,c} = full_adder(a3,b3,c)
    return {s3,s2,s1,s0,c}
end function
 
procedure test(integer a, integer b)
    bool {a0,a1,a2,a3} = int_to_bits(a,4),
         {b0,b1,b2,b3} = int_to_bits(b,4),
         {r3,r2,r1,r0,c} = four_bit_adder(a0,a1,a2,a3,b0,b1,b2,b3)
    integer r = bits_to_int({r0,r1,r2,r3})
    string s = iff(c?sprintf(" [=%d+16]",r):"")
    printf(1,"%04b + %04b = %04b %b (%d+%d=%d%s)\n",{a,b,r,c,a,b,c*16+r,s})
end procedure
 
test(0,0)
test(0,1)
test(0b1111,0b1111)
test(3,7)
test(11,8)
test(0b1100,0b1100)
test(0b1100,0b1101)
test(0b1100,0b1110)
test(0b1100,0b1111)
test(0b1101,0b0000)
test(0b1101,0b0001)
test(0b1101,0b0010)
test(0b1101,0b0011)
Output:
0000 + 0000 = 0000 0 (0+0=0)
0000 + 0001 = 0001 0 (0+1=1)
1111 + 1111 = 1110 1 (15+15=30 [=14+16])
0011 + 0111 = 1010 0 (3+7=10)
1011 + 1000 = 0011 1 (11+8=19 [=3+16])
1100 + 1100 = 1000 1 (12+12=24 [=8+16])
1100 + 1101 = 1001 1 (12+13=25 [=9+16])
1100 + 1110 = 1010 1 (12+14=26 [=10+16])
1100 + 1111 = 1011 1 (12+15=27 [=11+16])
1101 + 0000 = 1101 0 (13+0=13)
1101 + 0001 = 1110 0 (13+1=14)
1101 + 0010 = 1111 0 (13+2=15)
1101 + 0011 = 0000 1 (13+3=16 [=0+16])

PicoLisp

(de halfAdder (A B)  #> (Carry . Sum)
   (cons
      (and A B)
      (xor A B) ) )

(de fullAdder (A B C)  #> (Carry . Sum)
   (let (Ha1 (halfAdder C A)  Ha2 (halfAdder (cdr Ha1) B))
      (cons
         (or (car Ha1) (car Ha2))
         (cdr Ha2) ) ) )

(de 4bitsAdder (A4 A3 A2 A1  B4 B3 B2 B1)  #> (V S4 S3 S2 S1)
   (let
      (Fa1 (fullAdder A1 B1)
         Fa2 (fullAdder A2 B2 (car Fa1))
         Fa3 (fullAdder A3 B3 (car Fa2))
         Fa4 (fullAdder A4 B4 (car Fa3)) )
      (list
         (car Fa4)
         (cdr Fa4)
         (cdr Fa3)
         (cdr Fa2)
         (cdr Fa1) ) ) )
Output:
: (4bitsAdder NIL NIL NIL T  NIL NIL NIL T)
-> (NIL NIL NIL T NIL)

: (4bitsAdder NIL T NIL NIL  NIL NIL T T)
-> (NIL NIL T T T)

: (4bitsAdder NIL T T T  NIL T T T)
-> (NIL T T T NIL)

: (4bitsAdder T T T T  NIL NIL NIL T)
-> (T NIL NIL NIL NIL)

PL/I

/* 4-BIT ADDER */

TEST: PROCEDURE OPTIONS (MAIN);
   DECLARE CARRY_IN BIT (1) STATIC INITIAL ('0'B) ALIGNED;
   declare (m, n, sum)(4) bit(1) aligned;
   declare i fixed binary;

   get edit (m, n) (b(1));
   put edit (m, ' + ', n, ' = ') (4 b, a);

   do i = 4 to 1 by -1;
      call full_adder ((carry_in), m(i), n(i), sum(i), carry_in);
   end;
   put edit (sum) (b);

HALF_ADDER: PROCEDURE (IN1, IN2, SUM, CARRY);
   DECLARE (IN1, IN2, SUM, CARRY) BIT (1) ALIGNED;

   SUM = ( ^IN1 & IN2) | ( IN1 & ^IN2);
         /* Exclusive OR using only AND, NOT, OR. */
   CARRY = IN1 & IN2;

END HALF_ADDER;

FULL_ADDER: PROCEDURE (CARRY_IN, IN1, IN2, SUM, CARRY);
   DECLARE (CARRY_IN, IN1, IN2, SUM, CARRY) BIT (1) ALIGNED;
   DECLARE (SUM2, CARRY2) BIT (1) ALIGNED;

   CALL HALF_ADDER (CARRY_IN, IN1, SUM, CARRY);
   CALL HALF_ADDER (SUM, IN2, SUM2, CARRY2);
   SUM = SUM2;
   CARRY = CARRY | CARRY2;
END FULL_ADDER;

END TEST;

PowerShell

Using Bytes as Inputs

function bxor2 ( [byte] $a, [byte] $b )
{
    $out1 = $a -band ( -bnot $b )
    $out2 = ( -bnot $a ) -band $b
    $out1 -bor $out2
}

function hadder ( [byte] $a, [byte] $b )
{
    @{
        "S"=bxor2 $a $b
        "C"=$a -band $b
    }
}

function fadder ( [byte] $a, [byte] $b, [byte] $cd )
{
    $out1 = hadder $cd $a
    $out2 = hadder $out1["S"] $b
    @{
        "S"=$out2["S"]
        "C"=$out1["C"] -bor $out2["C"]
    }
}

function FourBitAdder ( [byte] $a, [byte] $b )
{
    $a0 = $a -band 1
    $a1 = ($a -band 2)/2
    $a2 = ($a -band 4)/4
    $a3 = ($a -band 8)/8
    $b0 = $b -band 1
    $b1 = ($b -band 2)/2
    $b2 = ($b -band 4)/4
    $b3 = ($b -band 8)/8
    $out1 = fadder $a0 $b0 0
    $out2 = fadder $a1 $b1 $out1["C"]
    $out3 = fadder $a2 $b2 $out2["C"]
    $out4 = fadder $a3 $b3 $out3["C"]
    @{
        "S"="{3}{2}{1}{0}" -f $out1["S"], $out2["S"], $out3["S"], $out4["S"]
        "V"=$out4["C"]
    }
}

FourBitAdder 3 5

FourBitAdder 0xA 5

FourBitAdder 0xC 0xB

[Convert]::ToByte((FourBitAdder 0xC 0xB)["S"],2)

Translation of C# code

The well-written C# code on this page can be translated without any modification into a .NET type by PowerShell.

$source = @'
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace RosettaCodeTasks.FourBitAdder
{
	public struct BitAdderOutput
	{
		public bool S { get; set; }
		public bool C { get; set; }
		public override string ToString ( )
		{
			return "S" + ( S ? "1" : "0" ) + "C" + ( C ? "1" : "0" );
		}
	}
	public struct Nibble
	{
		public bool _1 { get; set; }
		public bool _2 { get; set; }
		public bool _3 { get; set; }
		public bool _4 { get; set; }
		public override string ToString ( )
		{
			return ( _4 ? "1" : "0" )
				+ ( _3 ? "1" : "0" )
				+ ( _2 ? "1" : "0" )
				+ ( _1 ? "1" : "0" );
		}
	}
	public struct FourBitAdderOutput
	{
		public Nibble N { get; set; }
		public bool C { get; set; }
		public override string ToString ( )
		{
			return N.ToString ( ) + "c" + ( C ? "1" : "0" );
		}
	}

	public static class LogicGates
	{
		// Basic Gates
		public static bool Not ( bool A ) { return !A; }
		public static bool And ( bool A, bool B ) { return A && B; }
		public static bool Or ( bool A, bool B ) { return A || B; }
 
		// Composite Gates
		public static bool Xor ( bool A, bool B ) {	return Or ( And ( A, Not ( B ) ), ( And ( Not ( A ), B ) ) ); }
	}

	public static class ConstructiveBlocks
	{
		public static BitAdderOutput HalfAdder ( bool A, bool B )
		{
			return new BitAdderOutput ( ) { S = LogicGates.Xor ( A, B ), C = LogicGates.And ( A, B ) };
		}
 
		public static BitAdderOutput FullAdder ( bool A, bool B, bool CI )
		{
			BitAdderOutput HA1 = HalfAdder ( CI, A );
			BitAdderOutput HA2 = HalfAdder ( HA1.S, B );
 
			return new BitAdderOutput ( ) { S = HA2.S, C = LogicGates.Or ( HA1.C, HA2.C ) };
		}
 
		public static FourBitAdderOutput FourBitAdder ( Nibble A, Nibble B, bool CI )
		{
 
			BitAdderOutput FA1 = FullAdder ( A._1, B._1, CI );
			BitAdderOutput FA2 = FullAdder ( A._2, B._2, FA1.C );
			BitAdderOutput FA3 = FullAdder ( A._3, B._3, FA2.C );
			BitAdderOutput FA4 = FullAdder ( A._4, B._4, FA3.C );

			return new FourBitAdderOutput ( ) { N = new Nibble ( ) { _1 = FA1.S, _2 = FA2.S, _3 = FA3.S, _4 = FA4.S }, C = FA4.C };
		}

		public static void Test ( )
		{
			Console.WriteLine ( "Four Bit Adder" );
 
			for ( int i = 0; i < 256; i++ )
			{
				Nibble A = new Nibble ( ) { _1 = false, _2 = false, _3 = false, _4 = false };
				Nibble B = new Nibble ( ) { _1 = false, _2 = false, _3 = false, _4 = false };
				if ( (i & 1) == 1)
				{
					A._1 = true;
				}
				if ( ( i & 2 ) == 2 )
				{
					A._2 = true;
				}
				if ( ( i & 4 ) == 4 )
				{
					A._3 = true;
				}
				if ( ( i & 8 ) == 8 )
				{
					A._4 = true;
				}
				if ( ( i & 16 ) == 16 )
				{
					B._1 = true;
				}
				if ( ( i & 32 ) == 32)
				{
					B._2 = true;
				}
				if ( ( i & 64 ) == 64 )
				{
					B._3 = true;
				}
				if ( ( i & 128 ) == 128 )
				{
					B._4 = true;
				}
 
				Console.WriteLine ( "{0} + {1} = {2}", A.ToString ( ), B.ToString ( ), FourBitAdder( A, B, false ).ToString ( ) );

			}

			Console.WriteLine ( );
		}

	}
}
'@

Add-Type -TypeDefinition $source -Language CSharpVersion3
[RosettaCodeTasks.FourBitAdder.ConstructiveBlocks]::Test()
Output:
Four Bit Adder
0000 + 0000 = 0000c0
0001 + 0000 = 0001c0
0010 + 0000 = 0010c0
.
.
.
1101 + 1111 = 1100c1
1110 + 1111 = 1101c1
1111 + 1111 = 1110c1

Prolog

Using hi/lo symbols to represent binary. As this is a simulation, there is no real "arithmetic" happening.

% binary 4 bit adder chip simulation

b_not(in(hi), out(lo)) :- !.      % not(1) = 0
b_not(in(lo), out(hi)).           % not(0) = 1

b_and(in(hi,hi), out(hi)) :- !.   % and(1,1) = 1
b_and(in(_,_), out(lo)).          % and(anything else) = 0

b_or(in(hi,_), out(hi)) :- !.     % or(1,any) = 1
b_or(in(_,hi), out(hi)) :- !.     % or(any,1) = 1
b_or(in(_,_), out(lo)).           % or(anything else) = 0

b_xor(in(A,B), out(O)) :- 
    b_not(in(A), out(NotA)), b_not(in(B), out(NotB)),
    b_and(in(A,NotB), out(P)), b_and(in(NotA,B), out(Q)),
    b_or(in(P,Q), out(O)).

b_half_adder(in(A,B), s(S), c(C)) :-
    b_xor(in(A,B),out(S)), b_and(in(A,B),out(C)).

b_full_adder(in(A,B,Ci), s(S), c(C1)) :-
  b_half_adder(in(Ci, A), s(S0), c(C0)),
  b_half_adder(in(S0, B), s(S), c(C)),
  b_or(in(C0,C), out(C1)). 
  
b_4_bit_adder(in(A0,A1,A2,A3), in(B0,B1,B2,B3), out(S0,S1,S2,S3), c(V)) :-
  b_full_adder(in(A0,B0,lo), s(S0), c(C0)),
  b_full_adder(in(A1,B1,C0), s(S1), c(C1)),
  b_full_adder(in(A2,B2,C1), s(S2), c(C2)),
  b_full_adder(in(A3,B3,C2), s(S3), c(V)).

test_add(A,B,T) :-
  b_4_bit_adder(A, B, R, C),
  writef('%w + %w is %w %w  \t(%w)\n', [A,B,R,C,T]).

go :-
  test_add(in(hi,lo,lo,lo), in(hi,lo,lo,lo), '1 + 1 = 2'), 
  test_add(in(lo,hi,lo,lo), in(lo,hi,lo,lo), '2 + 2 = 4'),
  test_add(in(hi,lo,hi,lo), in(hi,lo,lo,hi), '5 + 9 = 14'), 
  test_add(in(hi,hi,lo,hi), in(hi,lo,lo,hi), '11 + 9 = 20'), 
  test_add(in(lo,lo,lo,hi), in(lo,lo,lo,hi), '8 + 8 = 16'),
  test_add(in(hi,hi,hi,hi), in(hi,lo,lo,lo), '15 + 1 = 16').
?- go.
in(hi,lo,lo,lo) + in(hi,lo,lo,lo) is out(lo,hi,lo,lo) c(lo)  	(1 + 1 = 2)
in(lo,hi,lo,lo) + in(lo,hi,lo,lo) is out(lo,lo,hi,lo) c(lo)  	(2 + 2 = 4)
in(hi,lo,hi,lo) + in(hi,lo,lo,hi) is out(lo,hi,hi,hi) c(lo)  	(5 + 9 = 14)
in(hi,hi,lo,hi) + in(hi,lo,lo,hi) is out(lo,lo,hi,lo) c(hi)  	(11 + 9 = 20)
in(lo,lo,lo,hi) + in(lo,lo,lo,hi) is out(lo,lo,lo,lo) c(hi)  	(8 + 8 = 16)
in(hi,hi,hi,hi) + in(hi,lo,lo,lo) is out(lo,lo,lo,lo) c(hi)  	(15 + 1 = 16)
true.

PureBasic

;Because no representation for a solitary bit is present, bits are stored as bytes.
;Output values from the constructive building blocks is done using pointers (i.e. '*').

Procedure.b notGate(x)
  ProcedureReturn ~x
EndProcedure

Procedure.b xorGate(x,y)
  ProcedureReturn  (x & notGate(y)) | (notGate(x) & y)
EndProcedure
 
Procedure halfadder(a, b, *sum.Byte, *carry.Byte)
  *sum\b = xorGate(a, b)
  *carry\b = a & b
EndProcedure
 
Procedure fulladder(a, b, c0, *sum.Byte, *c1.Byte)
  Protected sum_ac.b, carry_ac.b, carry_sb.b
  
  halfadder(c0, a, @sum_ac, @carry_ac)
  halfadder(sum_ac, b, *sum, @carry_sb)
  *c1\b = carry_ac | carry_sb
EndProcedure

Procedure fourbitsadder(a0, a1, a2, a3, b0, b1, b2, b3 , *s0.Byte, *s1.Byte, *s2.Byte, *s3.Byte, *v.Byte)
  Protected.b c1, c2, c3
  
  fulladder(a0, b0, 0,   *s0, @c1)
  fulladder(a1, b1, c1,  *s1, @c2)
  fulladder(a2, b2, c2,  *s2, @c3)
  fulladder(a3, b3, c3,  *s3, *v)
EndProcedure

;// Test implementation, map two 4-character strings to the inputs of the fourbitsadder() and display results
Procedure.s test_4_bit_adder(a.s,b.s)
  Protected.b s0, s1, s2, s3,  v, i
  Dim a.b(3)
  Dim b.b(3)
  For i = 0 To 3
    a(i) = Val(Mid(a, 4 - i, 1))
    b(i) = Val(Mid(b, 4 - i, 1))
  Next

  fourbitsadder(a(0), a(1), a(2), a(3), b(0), b(1), b(2), b(3), @s0, @s1, @s2, @s3, @v)
  ProcedureReturn a + " + " + b + " = " + Str(s3) + Str(s2) + Str(s1) + Str(s0) + " overflow " + Str(v)
EndProcedure

If OpenConsole()
  PrintN(test_4_bit_adder("0110","1110"))
  
  Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
  Input()
  CloseConsole()
EndIf
Output:
0110 + 1110 = 0100 overflow 1

Python

Individual boolean bits are represented by either 1, 0, True (interchangeable with 1), and False (same as zero). a bit of value None is sometimes used as a place-holder.

Python functions represent the building blocks of the circuit: a function parameter for each block input and individual block outputs are either a return of a single value or a return of a tuple of values - one for each block output. A single element tuple is not returned for a block with one output.

Python lists are used to represent bus's of multiple bits, and in this circuit, bit zero - the least significant bit of bus's, is at index zero of the list, (which will be printed as the left-most member of a list).

The repetitive connections of the full adder block, fa4, are achieved by using a for loop which could easily be modified to generate adders of any width. fa4's arguments are interpreted as indexable, ordered collections of values - usually lists but tuples would work too. fa4's outputs are the sum, s, as a list and the single bit carry.

Functions are provided to convert between integers and bus's and back; and the test routine shows how they can be used to translate between the normal Python values and those of the simulation.

def xor(a, b): return (a and not b) or (b and not a)

def ha(a, b): return xor(a, b), a and b     # sum, carry

def fa(a, b, ci):
    s0, c0 = ha(ci, a)
    s1, c1 = ha(s0, b)
    return s1, c0 or c1     # sum, carry

def fa4(a, b):
    width = 4
    ci = [None] * width
    co = [None] * width
    s  = [None] * width
    for i in range(width):
        s[i], co[i] = fa(a[i], b[i], co[i-1] if i else 0)
    return s, co[-1]

def int2bus(n, width=4):
    return [int(c) for c in "{0:0{1}b}".format(n, width)[::-1]]

def bus2int(b):
    return sum(1 << i for i, bit in enumerate(b) if bit)

def test_fa4():
    width = 4
    tot = [None] * (width + 1)
    for a in range(2**width):
        for b in range(2**width):
            tot[:width], tot[width] = fa4(int2bus(a), int2bus(b))
            assert a + b == bus2int(tot), "totals don't match: %i + %i != %s" % (a, b, tot)


if __name__ == '__main__':
   test_fa4()

Quackery

File:Xor in Quackery .png

Stack based languages such as Quackery have a simple correspondence between the words that constitute the language and logic gates and their wiring. This is illustrated in the stackflow diagram on the right, which shows the mapping between gates and wiring, and Quackery words in the definition of xor.

The wiring on the left hand side corresponds to the Quackery stack, which by convention builds up from left to right, so the rightmost item is the top of stack.

The first word, over is a stack management word, it places a copy of the second on stack on the top of the stack. The next word, not, takes one argument from the stack and leaves one result on the stack.

After this, over does its thing again, again working on the topmost items on the stack, and then and takes two arguments from the stack and returns one result to the stack. By convention, words other than stack management words consume their arguments. Words can take zero or more arguments, and leave zero or more results.

unrot is another stack management word, which moves the top of stack down below the third on stack, the third and second on stack becoming the second on stack and top of stack respectively. (The converse action is rot. It moves the third on stack to the top of stack.)

Finally not takes one item from the stack and returns one, and and or both take two items from the stack and return one, leaving one item. So we can see from the diagram that xor takes two items and returns one. The stack comment ( b b --> b ) reflects this, with the b's standing for "Boolean".

Looking further down the code, halfadder uses the word 2dup, which is equivalent to over over, and dip.

dip temporarily removes the top of stack from the stack, performs the word or nest (i.e. code wrapped in [ and ]; "nest" is Quackery jargon for a dynamic array) following it, then returns the top of stack. Here it is followed by the word xor, but it could be just as easily be followed by a stack management word, or a nest of stack management words. Quackery has a small set of stack management words, and dip extends their reach slightly further down the stack.

4bitadder is highly unusual in taking eight arguments from the stack and returning five. It would be better practice to group the eight arguments into two nests of four arguments, and return the four bit result as a nest, and the carry bit separately. However this is an opportunity to illustrate other ways that Quackery can deal with more items on the stack than the stack management words available can cope with.

The first is 4 pack reverse unpack. 4 pack, takes the top 4 arguments off the stack and puts them into a nest. reverse reverses the order of the items in a nest, and unpack does the opposite of 4 pack. If the stack contained 1 2 3 4 before performing 4 pack reverse unpack, it would contain 4 3 2 1 afterwards.

This is necessary, because moving four items from the stack to the ancillary stack temp using 4 times [ temp put ] and then bringing them back one at a time using temp take will reverse their order, so we preemptively reverse it to counteract that. It is desirable for the task for arguments to 4bitadder to be in most significant bit first order so that the intent of, for example, 1 1 0 0   1 1 0 0 4bitadder is immediately obvious.

The same reasoning applies to the second instance of 4 pack reverse; witheach iterates over a nest, placing each item in the nest (from left to right) on the stack before performing the word or nest that follows it. The fulladder within the nest needs to operate from least to most significant bit, as per the diagram in the task description.

swap is another stack management word. It swaps the top of stack and second on stack. (The 0 that it swaps under the reversed nest is a dummy carry bit to feed to the first performance of fulladder within the iterative loop.

Finally we reverse the top five items on the stack to make the top of stack the least significant bit and so on, and therefore consistent with the bit order of the arguments.

In conclusion, the use of a stack and stack management words to carry data from one word to the next shows how stack based programming languages can be seeing as using structured data-flow as well as using structured control-flow. (times and witheach are two of Quackery's control-flow words.) Thank you for reading to the end. I hope you have enjoyed this brief glimpse into the paradigm of stack based programming with Quackery.

  [ over not 
    over and
    unrot not 
    and or ]                  is xor       (                     a b --> a^b           )

  [ 2dup and 
    dip xor ]                 is halfadder (                     a b --> s c           )

  [ halfadder
    dip halfadder or ]        is fulladder (                   a b c --> s c           )

  [ 4 pack reverse unpack
    4 times [ temp put ]
    4 pack reverse 
    0 swap witheach
      [ temp take fulladder ]
    5 pack reverse unpack ]   is 4bitadder ( b3 b2 b1 b0 a3 a2 a1 a0 --> c s3 s2 s1 s0 )

    say "1100 + 1100 = "
    1 1 0 0  1 1 0 0 4bitadder
    5 pack witheach echo
    cr
    say "1100 + 1101 = "
    1 1 0 0  1 1 0 1 4bitadder
    5 pack witheach echo
    cr
    say "1100 + 1110 = "
    1 1 0 0  1 1 1 0 4bitadder
    5 pack witheach echo
    cr
    say "1100 + 1111 = "
    1 1 0 0  1 1 1 1 4bitadder
    5 pack witheach echo
    cr
    say "1101 + 0000 = "
    1 1 0 1  0 0 0 0 4bitadder
    5 pack witheach echo
    cr
    say "1101 + 0001 = "
    1 1 0 1  0 0 0 1 4bitadder
    5 pack witheach echo
    cr
    say "1101 + 0010 = "
    1 1 0 1  0 0 1 0 4bitadder
    5 pack witheach echo
    cr
    say "1101 + 0011 = "
    1 1 0 1  0 0 1 1 4bitadder
    5 pack witheach echo
    cr
Output:
1100 + 1100 = 11000
1100 + 1101 = 11001
1100 + 1110 = 11010
1100 + 1111 = 11011
1101 + 0000 = 01101
1101 + 0001 = 01110
1101 + 0010 = 01111
1101 + 0011 = 10000

Racket

#lang racket

(define (adder-and a b)
  (if (= 2 (+ a b)) 1 0))    ; Defining the basic and function

(define (adder-not a)
  (if (zero? a) 1 0))        ; Defining the basic not function

(define (adder-or a b)
  (if (> (+ a b) 0) 1 0))    ; Defining the basic or function

(define (adder-xor a b)
  (adder-or
   (adder-and
    (adder-not a)
    b)
   (adder-and
    a
    (adder-not b))))         ; Defines the xor function based on the basic functions

(define (half-adder a b)
  (list (adder-xor a b) (adder-and a b))) ; Creates the half adder, returning '(sum carry)

(define (adder a b c0)
  (define half-a (half-adder c0 a))
  (define half-b (half-adder (car half-a) b))
  (list
   (car half-b)
   (adder-or (cadr half-a) (cadr half-b))))  ; Creates the full adder, returns '(sum carry)

(define (n-bit-adder 4a 4b)   ; Creates the n-bit adder, it receives 2 lists of same length
  (let-values                 ; Lists of the form '([01]+)
      (((4s v)                ; for/fold form will return 2 values, receiving this here
        (for/fold ((S null) (c 0)) ;initializes the full sum and carry
          ((a (in-list (reverse 4a))) (b (in-list (reverse 4b))))
          ;here it prepares variables for summing each element, starting from the least important bits
          (define added
            (adder a b c))
          (values
           (cons (car added) S) ; changes S and c to it's new values in the next iteration
           (cadr added)))))
    (if (zero? v)
        4s
        (cons v 4s))))

(n-bit-adder '(1 0 1 0) '(0 1 1 1)) ;-> '(1 0 0 0 1)

Raku

(formerly Perl 6)

sub xor ($a, $b) { (($a and not $b) or (not $a and $b)) ?? 1 !! 0 }

sub half-adder ($a, $b) {
    return xor($a, $b), ($a and $b);
}

sub full-adder ($a, $b, $c0) {
    my ($ha0_s, $ha0_c) = half-adder($c0, $a);
    my ($ha1_s, $ha1_c) = half-adder($ha0_s, $b);
    return $ha1_s, ($ha0_c or $ha1_c);
}

sub four-bit-adder ($a0, $a1, $a2, $a3, $b0, $b1, $b2, $b3) {
    my ($fa0_s, $fa0_c) = full-adder($a0, $b0, 0);
    my ($fa1_s, $fa1_c) = full-adder($a1, $b1, $fa0_c);
    my ($fa2_s, $fa2_c) = full-adder($a2, $b2, $fa1_c);
    my ($fa3_s, $fa3_c) = full-adder($a3, $b3, $fa2_c);

    return $fa0_s, $fa1_s, $fa2_s, $fa3_s, $fa3_c;
}

{
    use Test;

    is four-bit-adder(1, 0, 0, 0, 1, 0, 0, 0), (0, 1, 0, 0, 0), '1 + 1 == 2';
    is four-bit-adder(1, 0, 1, 0, 1, 0, 1, 0), (0, 1, 0, 1, 0), '5 + 5 == 10';
    is four-bit-adder(1, 0, 0, 1, 1, 1, 1, 0)[4], 1, '7 + 9 == overflow';
}
Output:
ok 1 - 1 + 1 == 2
ok 2 - 5 + 5 == 10
ok 3 - 7 + 9 == overflow

REXX

Programming note:   REXX subroutines/functions are call by value, not call by name, so REXX has to expose a variable to make it global.

REXX programming syntax:

  • the     &&   symbol is an eXclusive OR function (XOR).
  • the     |       symbol is a logical OR.
  • the     &     symbol is a logical AND.
/*REXX program displays (all) the  sums  of a  full  4─bit adder  (with carry).         */
call hdr1;    call hdr2                          /*note the order of headers & trailers.*/
                                                 /* [↓]  traipse thru all possibilities.*/
   do    j=0  for 16
                             do m=0  for 4;   a.m= bit(j, m)
                             end   /*m*/
      do k=0  for 16
                             do m=0  for 4;   b.m= bit(k, m)
                             end   /*m*/
      sc= 4bitAdder(a., b.)
      z= a.3 a.2 a.1 a.0    '~+~'   b.3 b.2 b.1 b.0   "~=~"    sc   ','    s.3 s.2 s.1 s.0
      say translate( space(z, 0), , '~')         /*translate tildes (~) to blanks in Z. */
      end   /*k*/
   end      /*j*/

call hdr2;    call hdr1                          /*display two trailers (note the order)*/
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
bit:       procedure;  parse arg x,y;    return  substr( reverse( x2b( d2x(x) ) ), y+1, 1)
halfAdder: procedure expose c;   parse arg x,y;          c= x & y;           return x && y
hdr1:      say 'aaaa + bbbb = c, sum     [c=carry]';                         return
hdr2:      say '════   ════   ══════'              ;                         return
/*──────────────────────────────────────────────────────────────────────────────────────*/
fullAdder: procedure expose c;   parse arg x,y,fc
           #1= halfAdder(fc, x);        c1= c
           #2= halfAdder(#1, y);        c= c | c1;                           return #2
/*──────────────────────────────────────────────────────────────────────────────────────*/
4bitAdder: procedure expose s. a. b.;  carry.= 0
               do j=0  for 4;                 n= j - 1
               s.j= fullAdder(a.j, b.j, carry.n);        carry.j= c
               end   /*j*/;                                                  return c
output     (most lines have been elided):
aaaa + bbbb = c, sum     [c=carry]
════   ════   ══════
0000 + 0000 = 0,0000
0000 + 0001 = 0,0001
0000 + 0010 = 0,0010
0000 + 0011 = 0,0011
0000 + 0100 = 0,0100
0000 + 0101 = 0,0101
0000 + 0110 = 0,0110
0000 + 0111 = 0,0111
0000 + 1000 = 0,1000
0000 + 1001 = 0,1001 
 ∙
 ∙
 ∙ 
0101 + 0100 = 0,1001
0101 + 0101 = 0,1010
0101 + 0110 = 0,1011
0101 + 0111 = 0,1100
0101 + 1000 = 0,1101
0101 + 1001 = 0,1110
0101 + 1010 = 0,1111
0101 + 1011 = 1,0000
0101 + 1100 = 1,0001
0101 + 1101 = 1,0010
0101 + 1110 = 1,0011
0101 + 1111 = 1,0100
0110 + 0000 = 0,0110
0110 + 0001 = 0,0111
0110 + 0010 = 0,1000
0110 + 0011 = 0,1001
0110 + 0100 = 0,1010
0110 + 0101 = 0,1011
0110 + 0110 = 0,1100
0110 + 0111 = 0,1101
0110 + 1000 = 0,1110
0110 + 1001 = 0,1111
0110 + 1010 = 1,0000
0110 + 1011 = 1,0001
0110 + 1100 = 1,0010
0110 + 1101 = 1,0011
 ∙
 ∙
 ∙ 
1110 + 1110 = 1,1100
1110 + 1111 = 1,1101
1111 + 0000 = 0,1111
1111 + 0001 = 1,0000
1111 + 0010 = 1,0001
1111 + 0011 = 1,0010
1111 + 0100 = 1,0011
1111 + 0101 = 1,0100
1111 + 0110 = 1,0101
1111 + 0111 = 1,0110
1111 + 1000 = 1,0111
1111 + 1001 = 1,1000
1111 + 1010 = 1,1001
1111 + 1011 = 1,1010
1111 + 1100 = 1,1011
1111 + 1101 = 1,1100
1111 + 1110 = 1,1101
1111 + 1111 = 1,1110
════   ════   ══════
aaaa + bbbb = c, sum     [c=carry]

Ring

Template:Full One-Bit-Adder function is made up of XOR OR AND gates

###---------------------------
# Program: 4 Bit Adder - Ring
# Author:  Bert Mariani
# Date:    2018-02-28
# 
# Bit Adder: Input  A B Cin
#            Output S   Cout
#
# A ^ B => axb                XOR gate
#          axb ^ C => Sout    XOR gate
#          axb & C => d       AND gate
#
# A & B => anb                AND gate
#          anb | d => Cout     OR gate
# 
# Call Adder for number of bit in input fields
###-------------------------------------------
### 4 Bits

Cout     = "0" 
OutputS  = "0000"
InputA   = "0101"
InputB   = "1101"
 
   See "InputA:.. "+ InputA +nl
   See "InputB:.. "+ InputB +nl
BitsAdd(InputA, InputB)
   See "Sum...: "+ Cout +" "+ OutputS +nl+nl

###-------------------------------------------
### 32 Bits

Cout     = "0" 
OutputS  = "00000000000000000000000000000000"
InputA   = "01010101010101010101010101010101"
InputB   = "11011101110111011101110111011101"
 
   See "InputA:.. "+ InputA +nl
   See "InputB:.. "+ InputB +nl
BitsAdd(InputA, InputB)
   See "Sum...: "+ Cout +" "+ OutputS +nl+nl

###-------------------------------

Func BitsAdd(InputA, InputB)
	nbrBits = len(InputA)
	 
	for i = nbrBits to 1 step -1
	      A = InputA[i]
	      B = InputB[i]
	      C = Cout
  
              S = Adder(A,B,C)
	      OutputS[i] = "" + S
	next
return
  
###------------------------
Func Adder(A,B,C)
 
    axb  =   A ^ B
    Sout = axb ^ C
    d    = axb & C
 
    anb  =   A & B
    Cout = anb | d    ### Cout is global
 
return(Sout)
###------------------------

Output:


InputA:.. 0101
InputB:.. 1101
Sum...: 1 0010

InputA:.. 01010101010101010101010101010101
InputB:.. 11011101110111011101110111011101
Sum...: 1 00110011001100110011001100110010

RPL

Works with: HP version 28

To make a long piece of code short, on a 4-bit machine equipped with an interpreter capable to handle 64-bit integers, we reduce their size to 1 bit so that we can simulate the working of the 4-bit CPU at a very high level of software abstraction.

RPL code Comment
≪ → nibble 
  ≪ { } 1 nibble SIZE FOR j
        nibble j DUP SUB "1" == R→B + NEXT
≫ ≫ ‘-→LOAD’ STO

≪ → nibble carry
  ≪ "" 1 nibble SIZE FOR bit
        nibble bit GET B→R →STR + NEXT
     "→" + carry B→R →STR +
≫ ≫ ‘→DISP’ STO

≪ → a b 
  ≪ a b NOT AND b a NOT AND OR
≫ ≫ ‘→XOR’ STO

≪ → a b 
  ≪ a b →XOR a b AND
≫ ≫ ‘→HALF’ STO

≪ → a b c
  ≪ c a →HALF SWAP b →HALF ROT OR
≫ ≫ ‘→FULL’ STO

≪ 
   1 STWS
   →LOAD SWAP →LOAD → n2 n1
  ≪ { } #0h 4 1 FOR bit
        n1 bit GET n2 bit GET
        ROT →FULL
        SWAP ROT + SWAP
     -1 STEP →DISP
≫ ≫ ‘→ADD’ STO
→LOAD ( "nibble" → { #bits } ) 
turn the input format into a list of bits,
easier to handle


→DISP ( { #bits } c → "nibble→c" ) 
convert the bit list to a string




→XOR ( a b → xor(a,b) ) 
= (not a and b) or (not b and a)


→HALF ( a b → a+b carry ) 
s = (a xor b), c = (a and b)


→FULL ( a b c → a+b+c carry ) 



→ADD ( "nibble" "nibble" → "nibble→c" ) 
set unsigned integer size to 1 bit
convert strings into lists
from lower to higher bit
  read bits
  add them
  store result, keep carry
show result

"0101" "0011" →ADD
"1111" "1111" →ADD
Output:
2: "1000→0"
1: "1110→1"

Ruby

# returns pair [sum, carry]
def four_bit_adder(a, b)
  a_bits = binary_string_to_bits(a,4)
  b_bits = binary_string_to_bits(b,4)
  
  s0, c0 = full_adder(a_bits[0], b_bits[0],  0)
  s1, c1 = full_adder(a_bits[1], b_bits[1], c0)
  s2, c2 = full_adder(a_bits[2], b_bits[2], c1)
  s3, c3 = full_adder(a_bits[3], b_bits[3], c2)
  
  [bits_to_binary_string([s0, s1, s2, s3]), c3.to_s]
end

# returns pair [sum, carry]
def full_adder(a, b, c0)
  s, c = half_adder(c0, a)
  s, c1 = half_adder(s, b)
  [s, _or(c,c1)]
end

# returns pair [sum, carry]
def half_adder(a, b)
  [xor(a, b), _and(a,b)]
end

def xor(a, b)
  _or(_and(a, _not(b)), _and(_not(a), b))
end

# "and", "or" and "not" are Ruby keywords
def _and(a, b)  a & b  end
def _or(a, b)   a | b  end
def _not(a)    ~a & 1  end

def int_to_binary_string(n, length)
  "%0#{length}b" % n
end

def binary_string_to_bits(s, length)
  ("%#{length}s" % s).reverse.chars.map(&:to_i)
end

def bits_to_binary_string(bits)
  bits.map(&:to_s).reverse.join
end

puts " A    B      A      B   C    S  sum" 
0.upto(15) do |a|
  0.upto(15) do |b|
    bin_a = int_to_binary_string(a, 4)
    bin_b = int_to_binary_string(b, 4)
    sum, carry = four_bit_adder(bin_a, bin_b)
    puts "%2d + %2d = %s + %s = %s %s = %2d" %
         [a, b, bin_a, bin_b, carry, sum, (carry + sum).to_i(2)]
  end
end
Output:
 A    B      A      B   C    S  sum
 0 +  0 = 0000 + 0000 = 0 0000 =  0
 0 +  1 = 0000 + 0001 = 0 0001 =  1
 0 +  2 = 0000 + 0010 = 0 0010 =  2
 0 +  3 = 0000 + 0011 = 0 0011 =  3
 0 +  4 = 0000 + 0100 = 0 0100 =  4
...
 7 + 13 = 0111 + 1101 = 1 0100 = 20
 7 + 14 = 0111 + 1110 = 1 0101 = 21
 7 + 15 = 0111 + 1111 = 1 0110 = 22
 8 +  0 = 1000 + 0000 = 0 1000 =  8
 8 +  1 = 1000 + 0001 = 0 1001 =  9
 8 +  2 = 1000 + 0010 = 0 1010 = 10
...
15 + 12 = 1111 + 1100 = 1 1011 = 27
15 + 13 = 1111 + 1101 = 1 1100 = 28
15 + 14 = 1111 + 1110 = 1 1101 = 29
15 + 15 = 1111 + 1111 = 1 1110 = 30

Rust

// half adder with XOR and AND
// SUM = A XOR B
// CARRY = A.B
fn half_adder(a: usize, b: usize) -> (usize, usize) {
    return (a ^ b, a & b);
}

// full adder as a combination of half adders
// SUM = A XOR B XOR C
// CARRY = A.B + B.C + C.A
fn full_adder(a: usize, b: usize, c_in: usize) -> (usize, usize) {
    let (s0, c0) = half_adder(a, b);
    let (s1, c1) = half_adder(s0, c_in);
    return (s1, c0 | c1);
}

// A = (A3, A2, A1, A0)
// B = (B3, B2, B1, B0)
// S = (S3, S2, S1, S0)
fn four_bit_adder (
    a: (usize, usize, usize, usize),
    b: (usize, usize, usize, usize)
)
    ->
    // 4 bit output, carry is ignored
    (usize, usize, usize, usize)
{
    // lets have a.0 refer to the rightmost element
    let a = a.reverse();
    let b = b.reverse();

    // i would prefer a loop but that would abstract
    // the "connections of the constructive blocks"
    let (sum, carry) = half_adder(a.0, b.0);
    let out0 = sum;
    let (sum, carry) = full_adder(a.1, b.1, carry);
    let out1 = sum;
    let (sum, carry) = full_adder(a.2, b.2, carry);
    let out2 = sum;
    let (sum, _) = full_adder(a.3, b.3, carry);
    let out3 = sum;
    return (out3, out2, out1, out0);
}

fn main() {
    let a: (usize, usize, usize, usize) = (0, 1, 1, 0);
    let b: (usize, usize, usize, usize) = (0, 1, 1, 0);
    assert_eq!(four_bit_adder(a, b), (1, 1, 0, 0));
    // 0110 + 0110 = 1100
    // 6 + 6 = 12
}

// misc. traits to make our life easier
trait Reverse<A, B, C, D> {
    fn reverse(self) -> (D, C, B, A);
}

// reverse a generic tuple of arity 4
impl<A, B, C, D> Reverse<A, B, C, D> for (A, B, C, D) {
    fn reverse(self) -> (D, C, B, A){
        return (self.3, self.2, self.1, self.0)
    }
}

Sather

-- a "pin" can be connected only to one component
-- that "sets" it to 0 or 1, while it can be "read"
-- ad libitum. (Tristate logic is not taken into account)
-- This class does the proper checking, assuring the "circuit"
-- and the connections are described correctly. Currently can make
-- hard the implementation of a latch
class PIN is
  private attr v:INT;
  readonly attr name:STR;
  private attr connected:BOOL;

  create(n:STR):SAME is -- n = conventional name for this "pin"
    res ::= new;
    res.name := n;
    res.connected := false;
    return res;
  end;
  
  val:INT is
    if self.connected.not then
       #ERR + "pin " + self.name + " is undefined\n";
       return 0; -- could return a random bit to "simulate" undefined
                 -- behaviour
    else
       return self.v;
    end;
  end;

  -- connect ...
  val(v:INT) is
    if self.connected then
       #ERR + "pin " + self.name + " is already 'assigned'\n";
    else
       self.connected := true;
       self.v := v.band(1);
    end;
  end;

  -- connect to existing pin
  val(v:PIN) is
     self.val(v.val);
  end;
end;

-- XOR "block"
class XOR is
  readonly attr xor :PIN;

  create(a, b:PIN):SAME is
    res ::= new;
    res.xor := #PIN("xor output");
    l   ::= a.val.bnot.band(1).band(b.val);
    r   ::= a.val.band(b.val.bnot.band(1));
    res.xor.val := r.bor(l);
    return res;
  end;
end;

-- HALF ADDER "block"
class HALFADDER is
  readonly attr s, c:PIN;

  create(a, b:PIN):SAME is
    res ::= new;
    res.s := #PIN("halfadder sum output");
    res.c := #PIN("halfadder carry output");
    res.s.val := #XOR(a, b).xor.val;
    res.c.val := a.val.band(b.val);
    return res;
  end;
end;

-- FULL ADDER "block"
class FULLADDER is
  readonly attr s, c:PIN;

  create(a, b, ic:PIN):SAME is
    res ::= new;
    res.s := #PIN("fulladder sum output");
    res.c := #PIN("fulladder carry output");
    halfadder1 ::= #HALFADDER(a, b);
    halfadder2 ::= #HALFADDER(halfadder1.s, ic);
    res.s.val := halfadder2.s;
    res.c.val := halfadder2.c.val.bor(halfadder1.c.val);
    return res;
  end;
end;

-- FOUR BITS ADDER "block"
class FOURBITSADDER is
  readonly attr s0, s1, s2, s3, v :PIN;
  
  create(a0, a1, a2, a3, b0, b1, b2, b3:PIN):SAME is
    res ::= new;
    res.s0  := #PIN("4-bits-adder sum outbut line 0");
    res.s1  := #PIN("4-bits-adder sum outbut line 1");
    res.s2  := #PIN("4-bits-adder sum outbut line 2");
    res.s3  := #PIN("4-bits-adder sum outbut line 3");
    res.v   := #PIN("4-bits-adder overflow output");
    zero ::= #PIN("zero/mass pin");
    zero.val := 0;
    fa0 ::= #FULLADDER(a0, b0, zero);
    fa1 ::= #FULLADDER(a1, b1, fa0.c);
    fa2 ::= #FULLADDER(a2, b2, fa1.c);
    fa3 ::= #FULLADDER(a3, b3, fa2.c);
    res.v.val  := fa3.c;
    res.s0.val := fa0.s;
    res.s1.val := fa1.s;
    res.s2.val := fa2.s;
    res.s3.val := fa3.s;
    return res;
  end;
end;

-- testing --

class MAIN is
  main is
    a0 ::= #PIN("a0 in"); b0 ::= #PIN("b0 in");
    a1 ::= #PIN("a1 in"); b1 ::= #PIN("b1 in");
    a2 ::= #PIN("a2 in"); b2 ::= #PIN("b2 in");
    a3 ::= #PIN("a3 in"); b3 ::= #PIN("b3 in");
    ov ::= #PIN("overflow");

    a0.val := 1; b0.val := 1;
    a1.val := 1; b1.val := 1;
    a2.val := 0; b2.val := 0;
    a3.val := 0; b3.val := 1;

    fba ::= #FOURBITSADDER(a0,a1,a2,a3,b0,b1,b2,b3);
    #OUT + #FMT("%d%d%d%d", a3.val, a2.val, a1.val, a0.val) +
    	   " + " + 
           #FMT("%d%d%d%d", b3.val, b2.val, b1.val, b0.val) +
           " = " +
           #FMT("%d%d%d%d", fba.s3.val, fba.s2.val, fba.s1.val, fba.s0.val) + 
           ", overflow = " + fba.v.val + "\n";
  end;
end;

Scala

object FourBitAdder {
   type Nibble=(Boolean, Boolean, Boolean, Boolean)

   def xor(a:Boolean, b:Boolean)=(!a)&&b || a&&(!b)

   def halfAdder(a:Boolean, b:Boolean)={
      val s=xor(a,b)
      val c=a && b
      (s, c)
   }

   def fullAdder(a:Boolean, b:Boolean, cIn:Boolean)={
      val (s1, c1)=halfAdder(a, cIn)
      val (s, c2)=halfAdder(s1, b)
      val cOut=c1 || c2
      (s, cOut)
   }

   def fourBitAdder(a:Nibble, b:Nibble)={
      val (s0, c0)=fullAdder(a._4, b._4, false)
      val (s1, c1)=fullAdder(a._3, b._3, c0)
      val (s2, c2)=fullAdder(a._2, b._2, c1)
      val (s3, cOut)=fullAdder(a._1, b._1, c2)
      ((s3, s2, s1, s0), cOut)
   }
}

A test program using the object above.

object FourBitAdderTest {
   import FourBitAdder._
   def main(args: Array[String]): Unit = {
      println("%4s   %4s   %4s %2s".format("A","B","S","C"))
      for(a <- 0 to 15; b <- 0 to 15){
         val (s, cOut)=fourBitAdder(a,b)
         println("%4s + %4s = %4s %2d".format(nibbleToString(a),nibbleToString(b),nibbleToString(s),cOut.toInt))
      }
   }

   implicit def toInt(b:Boolean):Int=if (b) 1 else 0
   implicit def intToBool(i:Int):Boolean=if (i==0) false else true
   implicit def intToNibble(i:Int):Nibble=((i>>>3)&1, (i>>>2)&1, (i>>>1)&1, i&1)
   def nibbleToString(n:Nibble):String="%d%d%d%d".format(n._1.toInt, n._2.toInt, n._3.toInt, n._4.toInt)
}
Output:
   A      B      S  C
0000 + 0000 = 0000  0
0000 + 0001 = 0001  0
0000 + 0010 = 0010  0
0000 + 0011 = 0011  0
0000 + 0100 = 0100  0
...
1111 + 1011 = 1010  1
1111 + 1100 = 1011  1
1111 + 1101 = 1100  1
1111 + 1110 = 1101  1
1111 + 1111 = 1110  1

Scheme

Library: Scheme/SRFIs
Translation of: Common Lisp
(import (scheme base)
        (scheme write)
        (srfi 60))      ;; for logical bits

;; Returns a list of bits: '(sum carry)
(define (half-adder a b)
  (list (bitwise-xor a b) (bitwise-and a b)))

;; Returns a list of bits: '(sum carry)
(define (full-adder a b c-in)
  (let* ((h1 (half-adder c-in a))
         (h2 (half-adder (car h1) b)))
    (list (car h2) (bitwise-ior (cadr h1) (cadr h2)))))

;; a and b are lists of 4 bits each
(define (four-bit-adder a b)
  (let* ((add-1 (full-adder (list-ref a 3) (list-ref b 3) 0))
         (add-2 (full-adder (list-ref a 2) (list-ref b 2) (list-ref add-1 1)))
         (add-3 (full-adder (list-ref a 1) (list-ref b 1) (list-ref add-2 1)))
         (add-4 (full-adder (list-ref a 0) (list-ref b 0) (list-ref add-3 1))))
    (list (list (car add-4) (car add-3) (car add-2) (car add-1))
          (cadr add-4))))

(define (show-eg a b)
  (display a) (display " + ") (display b) (display " = ") 
  (display (four-bit-adder a b)) (newline))

(show-eg (list 0 0 0 0) (list 0 0 0 0))
(show-eg (list 0 0 0 0) (list 1 1 1 1))
(show-eg (list 1 1 1 1) (list 0 0 0 0))
(show-eg (list 0 1 0 1) (list 1 1 0 0))
(show-eg (list 1 1 1 1) (list 1 1 1 1))
(show-eg (list 1 0 1 0) (list 0 1 0 1))
Output:
(0 0 0 0) + (0 0 0 0) = ((0 0 0 0) 0)
(0 0 0 0) + (1 1 1 1) = ((1 1 1 1) 0)
(1 1 1 1) + (0 0 0 0) = ((1 1 1 1) 0)
(0 1 0 1) + (1 1 0 0) = ((0 0 0 1) 1)
(1 1 1 1) + (1 1 1 1) = ((1 1 1 0) 1)
(1 0 1 0) + (0 1 0 1) = ((1 1 1 1) 0)

Sed

This is full adder that means it takes arbitrary number of bits (think of it as infinite stack of 2 bit adders, which is btw how it's internally made). I took it from https://github.com/emsi/SedScripts

#!/bin/sed -f
# (C) 2005,2014 by Mariusz Woloszyn :)
# https://en.wikipedia.org/wiki/Adder_(electronics)

##############################
# PURE SED BINARY FULL ADDER #
##############################


# Input two lines, sanitize input
N
s/ //g
/^[01	 ]\+\n[01	 ]\+$/! {
	i\
	ERROR: WRONG INPUT DATA
	d
	q
}
s/[ 	]//g

# Add place for Sum and Cary bit
s/$/\n\n0/

:LOOP
# Pick A,B and C bits and put that to hold
s/^\(.*\)\(.\)\n\(.*\)\(.\)\n\(.*\)\n\(.\)$/0\1\n0\3\n\5\n\6\2\4/
h

# Grab just A,B,C
s/^.*\n.*\n.*\n\(...\)$/\1/

# binary full adder module
# INPUT:  3bits (A,B,Carry in), for example 101
# OUTPUT: 2bits (Carry, Sum), for wxample   10
s/$/;000=00001=01010=01011=10100=01101=10110=10111=11/
s/^\(...\)[^;]*;[^;]*\1=\(..\).*/\2/

# Append the sum to hold
H

# Rewrite the output, append the sum bit to final sum
g
s/^\(.*\)\n\(.*\)\n\(.*\)\n...\n\(.\)\(.\)$/\1\n\2\n\5\3\n\4/

# Output result and exit if no more bits to process..
/^\([0]*\)\n\([0]*\)\n/ {
	s/^.*\n.*\n\(.*\)\n\(.\)/\2\1/
	s/^0\(.*\)/\1/
	q
}

b LOOP

Example usage:

./binAdder.sed
1111110111
1
1111111000

./binAdder.sed
10
10001
10011

./binAdder.sed
0 1 1 0
0 0 0 1
111

Sidef

Translation of: Perl
func bxor(a, b) {
  (~a & b) | (a & ~b)
}

func half_adder(a, b) {
  return (bxor(a, b), a & b)
}

func full_adder(a, b, c) {
  var (s1, c1) = half_adder(a, c)
  var (s2, c2) = half_adder(s1, b)
  return (s2, c1 | c2)
}

func four_bit_adder(a, b) {
  var (s0, c0) = full_adder(a[0], b[0], 0)
  var (s1, c1) = full_adder(a[1], b[1], c0)
  var (s2, c2) = full_adder(a[2], b[2], c1)
  var (s3, c3) = full_adder(a[3], b[3], c2)
  return ([s3,s2,s1,s0].join, c3.to_s)
}

say " A    B      A      B   C    S  sum"
for a in ^16 {
  for b in ^16 {
    var(abin, bbin) = [a,b].map{|n| "%04b"%n->chars.reverse.map{.to_i} }...
    var(s, c) = four_bit_adder(abin, bbin)
    printf("%2d + %2d = %s + %s = %s %s = %2d\n",
        a, b, abin.join, bbin.join, c, s, "#{c}#{s}".bin)
    }
}
Output:
 A    B      A      B   C    S  sum
 0 +  0 = 0000 + 0000 = 0 0000 =  0
 0 +  1 = 0000 + 0001 = 0 0001 =  1
 0 +  2 = 0000 + 0010 = 0 0010 =  2
 0 +  3 = 0000 + 0011 = 0 0011 =  3
 0 +  4 = 0000 + 0100 = 0 0100 =  4
...
 7 + 13 = 0111 + 1101 = 1 0100 = 20
 7 + 14 = 0111 + 1110 = 1 0101 = 21
 7 + 15 = 0111 + 1111 = 1 0110 = 22
 8 +  0 = 1000 + 0000 = 0 1000 =  8
 8 +  1 = 1000 + 0001 = 0 1001 =  9
 8 +  2 = 1000 + 0010 = 0 1010 = 10
...
15 + 12 = 1111 + 1100 = 1 1011 = 27
15 + 13 = 1111 + 1101 = 1 1100 = 28
15 + 14 = 1111 + 1110 = 1 1101 = 29
15 + 15 = 1111 + 1111 = 1 1110 = 30

Swift

typealias FourBit = (Int, Int, Int, Int)

func halfAdder(_ a: Int, _ b: Int) -> (Int, Int) {
  return (a ^ b, a & b)
}

func fullAdder(_ a: Int, _ b: Int, carry: Int) -> (Int, Int) {
  let (s0, c0) = halfAdder(a, b)
  let (s1, c1) = halfAdder(s0, carry)

  return (s1, c0 | c1)
}

func fourBitAdder(_ a: FourBit, _ b: FourBit) -> (FourBit, carry: Int) {
  let (sum1, carry1) = halfAdder(a.3, b.3)
  let (sum2, carry2) = fullAdder(a.2, b.2, carry: carry1)
  let (sum3, carry3) = fullAdder(a.1, b.1, carry: carry2)
  let (sum4, carryOut) = fullAdder(a.0, b.0, carry: carry3)

  return ((sum4, sum3, sum2, sum1), carryOut)
}

let a = (0, 1, 1, 0)
let b = (0, 1, 1, 0)

print("\(a) + \(b) = \(fourBitAdder(a, b))")
Output:
(0, 1, 1, 0) + (0, 1, 1, 0) = ((1, 1, 0, 0), carry: 0)

SystemVerilog

In SystemVerilog we can define a multibit adder as a parameterized module, that instantiates the components:

module Half_Adder( input a, b, output s, c );
  assign s = a ^ b;
  assign c = a & b;
endmodule

module Full_Adder( input a, b, c_in, output s, c_out );

  wire s_ha1, c_ha1, c_ha2;

  Half_Adder ha1( .a(c_in), .b(a), .s(s_ha1), .c(c_ha1) );
  Half_Adder ha2( .a(s_ha1), .b(b), .s(s), .c(c_ha2)