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 a 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.
| Xor gate done with ands, ors and nots | A half adder | A full adder | A 4-bit adder |
|---|---|---|---|
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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).
Ada
<lang 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; </lang> A test program with the above definitions <lang Ada> 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; </lang>
- 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
AutoHotkey
<lang AutoHotkey>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 }</lang>
- Output:
13 + 9: 1101 + 1001 = 0110 (Carry = 1)
AutoIt
Functions
<lang AutoIt> 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 </lang>
Example
<lang AutoIt> 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) </lang>
- Output:
result: 1010 ==> carry out: 0 result: 0011 ==> carry out: 1
--BugFix (talk) 17:10, 14 November 2013 (UTC)
Batch File
<lang dos> @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 </lang>
- Output:
First 4-Bit Binary Number: 1011 Second 4-Bit Binary Number: 0111 1011 + 0111 = 10010
BASIC
Applesoft BASIC
<lang 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</lang>
BBC BASIC
<lang bbcbasic> @% = 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&</lang>
- 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
C
<lang 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;
}</lang>
C++
C#
<lang csharp> 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 ( ); }
} }
</lang>
Clojure
<lang 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) </lang>
Second Clojure solution
<lang clojure>(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]
)
</lang>
Using Bitwise Operators
<lang clojure> (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))))
</lang>
COBOL
<lang 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.
</lang>
- 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.
<lang coffeescript>
- 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] </lang>
Common Lisp
<lang 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) </lang> 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. <lang d>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);
}</lang>
- 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: <lang d>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);
}</lang>
- 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): <lang asm>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</lang>
Elixir
<lang elixir>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</lang>
- 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. <lang Erlang> -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). </lang>
- Output:
28> four_bit_adder:task().
{[0,1,0,1],0}
Forth
<lang 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 ;</lang>
- Output:
1 1 0 0 0 0 1 1 .add4 01111 ok
Fortran
<lang fortran>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</lang>
- 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
F#
<lang fsharp> 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" </lang>
- Output:
0001 + 0111 = (Zero, One, Zero, Zero,
Go
Bytes
Go does not have a bit type, so byte is used. This is the straightforward solution using bytes and functions. <lang go>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))
}</lang>
- Output:
1 0 0 1 1
Channels
Alternative solution is a little more like a simulation. <lang go>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]) } </lang>
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.
Haskell
Basic gates: <lang haskell>import Control.Arrow import Data.List (mapAccumR)
bor, band :: Int -> Int -> Int bor = max band = min bnot :: Int -> Int bnot = (1-)</lang> Gates built with basic ones: <lang haskell>nand, xor :: Int -> Int -> Int nand = (bnot.).band xor a b = uncurry nand. (nand a &&& nand b) $ nand a b</lang> Adder circuits: <lang haskell>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</lang>
Example using adder4 <lang haskell>*Main> adder4 [1,0,1,0] [1,1,1,1] (1,[1,0,0,1])</lang>
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.
<lang unicon>#
- 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</lang>
- 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
<lang j>and=: *. or=: +. not=: -. xor=: (and not) or (and not)~ hadd=: and ,"0 xor add=: ((({.,0:)@[ or {:@[ hadd {.@]), }.@])/@hadd</lang>
Example use
<lang j> 1 1 1 1 add 0 1 1 1 1 0 1 1 0</lang>
To produce all results: <lang j> add"1/~#:i.16</lang>
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:
<lang j> ,"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</lang>
Alternatively, the fact that add was designed to operate on lists of bits could have been incorporated into its definition:
<lang j>add=: ((({.,0:)@[ or {:@[ hadd {.@]), }.@])/@hadd"1</lang>
Then to get all results you could use: <lang j> add/~#:i.16</lang>
Compare this to a regular addition table: <lang j> +/~i.10</lang> (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
<lang 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;
}
}</lang>
- 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.
<lang JavaScript> 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;
} </lang>
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.
<lang JavaScript> // 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();
} </lang>
Example Use
<lang JavaScript>fourBitAdder('1010', '0101'); // 1111 (15)</lang>
all results:
<lang JavaScript> // 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;
} </lang>
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).
<lang jq># 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("") ;</lang>
Example: <lang jq>fourBitAdder("0111"; "0001")</lang>
- Output:
$ jq -n -f Four_bit_adder.jq "1000"
Jsish
Based on Javascript entry. <lang javascript>#!/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!
- /</lang>
- 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 <lang Julia>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)), "") </lang>
Main <lang Julia> 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 </lang>
- 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
<lang scala>// 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)
}
}</lang>
- 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.
Half Adder
Full Adder
4bit Adder
Lua
<lang 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)</lang> Output:
SUM OVERFLOW 0010 false 1111 false 1111 false 0000 true
M2000 Interpreter
<lang 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 </lang>
Mathematica / Wolfram Language
<lang>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}];</lang>
Example: <lang>fourbitadder[{1, 0, 1, 0}, {1, 1, 1, 1}]</lang> 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.
<lang MATLAB>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</lang>
Sample Usage: <lang MATLAB>>> [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</lang>
MUMPS
<lang 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</lang>
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 recent copy of Python, and the MyHDL library from myhdl.org. Both examples integrate test code, and export Verilog and VHDL for hardware synthesis.
Verbose Code - With integrated Test & Demo
<lang python>#!/usr/bin/env python
""" http://rosettacode.org/wiki/Four_bit_adder
Demonstrate theoretical four bit adder simulation
using And, Or & Invert primitives
2011-05-10 jc
"""
from myhdl import always_comb, ConcatSignal, delay, intbv, Signal, \
Simulation, toVerilog, toVHDL
from random import randrange
""" define set of primitives
------------------------ """
def inverter(z, a): # define component name & interface
""" z <- not(a) """
@always_comb # define asynchronous logic
def logic():
z.next = not a
return logic # return defined logic, named 'inverter'
def and2(z, a, b):
""" z <- a and b """
@always_comb
def logic():
z.next = a and b
return logic
def or2(z, a, b):
""" z <- a or b """
@always_comb
def logic():
z.next = a or b
return logic
""" build components using defined primitive set
-------------------------------------------- """
def xor2 (z, a, b):
""" z <- a xor b """ # define interconnect signals nota, notb, annotb, bnnota = [Signal(bool(0)) for i in range(4)] # name sub-components, and their interconnect inv0 = inverter(nota, a) inv1 = inverter(notb, b) and2a = and2(annotb, a, notb) and2b = and2(bnnota, b, nota) or2a = or2(z, annotb, bnnota) return inv0, inv1, and2a, and2b, or2a
def halfAdder(carry, summ, in_a, in_b):
""" carry,sum is the sum of in_a, in_b """ and2a = and2(carry, in_a, in_b) xor2a = xor2(summ, in_a, in_b) return and2a, xor2a
def fullAdder(fa_c1, fa_s, fa_c0, fa_a, fa_b):
""" fa_c0,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(ha1_c1, ha1_s, fa_c0, fa_a) halfAdder02 = halfAdder(ha2_c1, fa_s, ha1_s, fa_b) or2a = or2(fa_c1, ha1_c1, ha2_c1) return halfAdder01, halfAdder02, or2a
def Adder4b_ST(co,sum4, ina,inb):
assemble 4 full adders
c = [Signal(bool()) for i in range(0,4)]
sl = [Signal(bool()) for i in range(4)] # sum list
halfAdder_0 = halfAdder(c[1],sl[0], ina(0),inb(0))
fullAdder_1 = fullAdder(c[2],sl[1], c[1],ina(1),inb(1))
fullAdder_2 = fullAdder(c[3],sl[2], c[2],ina(2),inb(2))
fullAdder_3 = fullAdder(co, sl[3], c[3],ina(3),inb(3))
# create an internal bus for the output list
sc = ConcatSignal(*reversed(sl)) # create internal bus for output list
@always_comb
def list2intbv():
sum4.next = sc # assign internal bus to actual output
return halfAdder_0, fullAdder_1, fullAdder_2, fullAdder_3, 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)]
def test():
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
print
""" instantiate components and run test
----------------------------------- """
Adder4b_01 = Adder4b_ST(t_co,sum4, ina4,inb4) test_1 = test()
def main():
sim = Simulation(Adder4b_01, test_1) sim.run() toVHDL(Adder4b_ST, t_co,sum4, ina4,inb4) toVerilog(Adder4b_ST, t_co,sum4, ina4,inb4)
if __name__ == '__main__':
main()
</lang>
Professional Code - with test bench
<lang python>#!/usr/bin/env python
from myhdl import *
def Half_adder(a, b, s, c):
@always_comb
def logic():
s.next = a ^ b
c.next = a & b
return logic
def Full_Adder(a, b, cin, s, c_out):
s_ha1, c_ha1, c_ha2 = [Signal(bool()) for i in range(3)] ha1 = Half_adder(a=cin, b=a, s=s_ha1, c=c_ha1) ha2 = Half_adder(a=s_ha1, b=b, s=s, c=c_ha2)
@always_comb
def logic():
c_out.next = c_ha1 | c_ha2
return ha1, ha2, logic
def Multibit_Adder(a, b, s):
N = len(s)-1 # convert input busses to lists al = [a(i) for i in range(N)] bl = [b(i) for i in range(N)] # set up lists for carry and output cl = [Signal(bool()) for i in range(N+1)] sl = [Signal(bool()) for i in range(N+1)] # boundaries for carry and output cl[0] = 0 sl[N] = cl[N] # create an internal bus for the output list sc = ConcatSignal(*reversed(sl))
# assign internal bus to actual output
@always_comb
def assign():
s.next = sc
# create a list of adders
add = [None] * N
for i in range(N):
add[i] = Full_Adder(a=al[i], b=bl[i], s=sl[i], cin=cl[i], c_out=cl[i+1])
return add, assign
- declare I/O for a four-bit adder
N=4 a = Signal(intbv(0)[N:]) b = Signal(intbv(0)[N:]) s = Signal(intbv(0)[N+1:])
- convert to Verilog and VHDL
toVerilog(Multibit_Adder, a, b, s) toVHDL(Multibit_Adder, a, b, s)
- set up a test bench
from random import randrange def tb():
dut = Multibit_Adder(a, b, s)
@instance
def check():
yield delay(10)
for i in range(100):
p, q = randrange(2**N), randrange(2**N)
a.next = p
b.next = q
yield delay(10)
assert s == p + q
return dut, check
- the entry point for the py.test unit test framework
def test_Adder():
sim = Simulation(tb()) sim.run()
</lang>
Nim
<lang nim>proc ha(a, b): auto = [a xor b, a and b] # sum, carry
proc fa(a, b, ci): auto =
let a = ha(ci, a) let b = ha(a[0], b) [b[0], a[1] or b[1]] # sum, carry
proc fa4(a,b): array[5, bool] =
var co,s: array[4, bool] 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): array[4, bool] =
var n = n for i in 0..result.high: result[i] = (n and 1) == 1 n = n shr 1
proc bus2int(b): 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))</lang>
OCaml
<lang 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);; </lang>
Testing
<lang ocaml>
- 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) </lang>
An extension : n-bit adder, for n <= 64 (n could be greater, but we use Int64 for I/O)
<lang ocaml> (* 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);; </lang>
And a test
<lang ocaml>
- gen_plus 7 100 100;;
- : int * int = (72, 1)
- gen_plus 8 100 100;;
- : int * int = (200, 0) </lang>
PARI/GP
<lang parigp>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)</lang>
Perl
<lang 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.$s);
}
}</lang>
Output matches the Ruby output.
Perl 6
<lang perl6>sub xor ($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';
}</lang>
- Output:
ok 1 - 1 + 1 == 2 ok 2 - 5 + 5 == 10 ok 3 - 7 + 9 == overflow
Phix
<lang Phix>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)
bool 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)
bool {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)
bool {b0,b1,b2,b3} = int_to_bits(b,4)
bool {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})
printf(1,"%04b + %04b = %04b %b (%d+%d=%d)\n",{a,b,r,c,a,b,c*16+r})
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)</lang>
- Output:
0000 + 0000 = 0000 0 (0+0=0) 0000 + 0001 = 0001 0 (0+1=1) 1111 + 1111 = 1110 1 (15+15=30) 0011 + 0111 = 1010 0 (3+7=10) 1011 + 1000 = 0011 1 (11+8=19) 1100 + 1100 = 1000 1 (12+12=24) 1100 + 1101 = 1001 1 (12+13=25) 1100 + 1110 = 1010 1 (12+14=26) 1100 + 1111 = 1011 1 (12+15=27) 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)
PicoLisp
<lang 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) ) ) )</lang>
- 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
<lang 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; </lang>
PowerShell
Using Bytes as Inputs
<lang Powershell>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)</lang>
Translation of C# code
The well-written C# code on this page can be translated without any modification into a .NET type by PowerShell. <lang 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 </lang> <lang PowerShell> [RosettaCodeTasks.FourBitAdder.ConstructiveBlocks]::Test() </lang>
- 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. <lang prolog>% 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').</lang>
?- 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
<lang 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</lang>
- 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.
<lang python>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()</lang>
Racket
<lang 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)</lang>
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.
<lang rexx>/*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), , '_') /*remove all the underbars (_) from Z. */
end /*k*/
end /*j*/
call hdr2; call hdr1 /*display two trailers (note the order)*/ exit /*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</lang>
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
<lang ring>
- ---------------------------
- 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)
- ------------------------
</lang> Output:
InputA:.. 0101 InputB:.. 1101 Sum...: 1 0010 InputA:.. 01010101010101010101010101010101 InputB:.. 11011101110111011101110111011101 Sum...: 1 00110011001100110011001100110010
Ruby
<lang 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</lang>
- 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
<lang 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)
}
}
</lang>
Sather
<lang 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;</lang>
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 <lang sed>
- !/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</lang>
Example usage:
<lang sed> ./binAdder.sed 1111110111 1 1111111000
./binAdder.sed 10 10001 10011
./binAdder.sed 0 1 1 0 0 0 0 1 111 </lang>
Scala
<lang 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)
}
}</lang>
A test program using the object above. <lang scala>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)
}</lang>
- 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
<lang scheme> (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)) </lang>
- 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)
Sidef
<lang ruby>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)
}
}</lang>
- 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
SystemVerilog
In SystemVerilog we can define a multibit adder as a parameterized module, that instantiates the components: <lang SystemVerilog> 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) ); assign c_out = c_ha1 | c_ha2;
endmodule
module Multibit_Adder(a,b,s);
parameter N = 8; input [N-1:0] a; input [N-1:0] b; output [N:0] s;
wire [N:0] c;
assign c[0] = 0; assign s[N] = c[N];
generate genvar I; for (I=0; I<N; ++I) Full_Adder add( .a(a[I]), .b(b[I]), .s(s[I]), .c_in(c[I]), .c_out(c[I+1]) ); endgenerate
endmodule </lang>
And then a testbench to test it -- here I use random stimulus with an assertion (it's aften good to separate the stimulus generation from the results-checking):
<lang SystemVerilog> module simTop();
bit [3:0] a; bit [3:0] b; bit [4:0] s;
Multibit_Adder#(4) adder(.*);
always_comb begin $display( "%d + %d = %d", a, b, s ); assert( s == a+b ); end
endmodule
program Main();
class Test; rand bit [3:0] a; rand bit [3:0] b; endclass
Test t = new; initial repeat (20) begin #10 t.randomize; simTop.a = t.a; simTop.b = t.b; end
endprogram
</lang>
- Output:
0 + 0 = 0 7 + 0 = 7 11 + 3 = 14 9 + 15 = 24 7 + 3 = 10 1 + 4 = 5 9 + 7 = 16 10 + 6 = 16 15 + 9 = 24 9 + 3 = 12 2 + 3 = 5 14 + 5 = 19 1 + 8 = 9 0 + 4 = 4 13 + 9 = 22 15 + 7 = 22 3 + 15 = 18 7 + 4 = 11 13 + 4 = 17 10 + 7 = 17 1 + 2 = 3 $finish at simulation time 200
A quick note on the use of random stimulus. You might think that, with an input space of only 2**8 (256) distinct inputs, that exhaustive testing (i.e. just loop through all the possible inputs) would be appropriate. In this case you might be right. But as a HW verification engineer I'm used to dealing with coverage spaces closer to 10**80 (every state element -- bit of memory) increases the space). It's not practical to verify such hardware exhaustively -- indeed, it's hard to know where the interesting cases are -- so we use constrained random verification. If you want to, to can work thought the statistics to figure out the probability that we missed a bug when sampling 20 cases from a space of 2**8 -- it's quite scary when you realize that every complex digital chip that you ever bought (cpu, gpu, networking, etc.) was 0% verified (zero to at least 50 decimal places).
For a problem this small, however, we'd probably just whip out a "formal" tool and statically prove that the assertion can never fire for all possible sets of inputs.
Tcl
This example shows how you can make little languages in Tcl that describe the problem space. <lang tcl>package require Tcl 8.5
- Create our little language
proc pins args {
# Just declaration...
foreach p $args {upvar 1 $p v}
} proc gate {name pins body} {
foreach p $pins {
lappend args _$p append v " \$_$p $p"
} proc $name $args "upvar 1 $v;$body"
}
- Fundamental gates; these are the only ones that use Tcl math ops
gate not {x out} {
set out [expr {1 & ~$x}]
} gate and {x y out} {
set out [expr {$x & $y}]
} gate or {x y out} {
set out [expr {$x | $y}]
} gate GND pin {
set pin 0
}
- Composite gates: XOR
gate xor {x y out} {
pins nx ny x_ny nx_y
not x nx not y ny and x ny x_ny and nx y nx_y or x_ny nx_y out
}
- Composite gates: half adder
gate halfadd {a b sum carry} {
xor a b sum and a b carry
}
- Composite gates: full adder
gate fulladd {a b c0 sum c1} {
pins sum_ac carry_ac carry_sb
halfadd c0 a sum_ac carry_ac halfadd sum_ac b sum carry_sb or carry_ac carry_sb c1
}
- Composite gates: 4-bit adder
gate 4add {a0 a1 a2 a3 b0 b1 b2 b3 s0 s1 s2 s3 v} {
pins c0 c1 c2 c3
GND c0 fulladd a0 b0 c0 s0 c1 fulladd a1 b1 c1 s1 c2 fulladd a2 b2 c2 s2 c3 fulladd a3 b3 c3 s3 v
}</lang>
<lang tcl># Simple driver for the circuit proc 4add_driver {a b} {
lassign [split $a {}] a3 a2 a1 a0
lassign [split $b {}] b3 b2 b1 b0
lassign [split 00000 {}] s3 s2 s1 s0 v
4add a0 a1 a2 a3 b0 b1 b2 b3 s0 s1 s2 s3 v
return "$s3$s2$s1$s0 overflow=$v"
} set a 1011 set b 0110 puts $a+$b=[4add_driver $a $b]</lang>
- Output:
1011+0110=0001 overflow=1
One feature of the Tcl code is that if you change the definitions of and, or, not and GND (as well as of gate and pins, of course) you could have this Tcl code generate hardware for the adder. The bulk of the code would be identical.
TorqueScript
<lang Torque>function XOR(%a, %b) { return (!%a && %b) || (%a && !%b); }
//Seperated by space function HalfAdd(%a, %b) { return XOR(%a, %b) SPC %a && %b; }
//First word is the carry bit function FullAdd(%a, %b, %c0) { %r1 = HalfAdd(%a, %c0); %r2 = HalfAdd(getWord(%r1, 0), %b); %r3 = getWord(%r1, 1) || getWord(%r2, 1); return %r3 SPC getWord(%r2, 0); }
//Outputs each bit seperated by a space. function FourBitFullAdd(%a0, %a1, %a2, %a3, %b0, %b1, %b2, %b3) { %r0 = FullAdd(%a0, %b0, 0); %r1 = FullAdd(%a1, %b1, getWord(%r0, 0)); %r2 = FullAdd(%a2, %b2, getWord(%r1, 0)); %r3 = FullAdd(%a3, %b3, getWord(%r2, 0)); return getWord(%r0,1) SPC getWord(%r1,1) SPC getWord(%r2,1) SPC getWord(%r3,1) SPC getWord(%r3,0); }</lang>
Verilog
In Verilog we can also define a multibit adder as a component with multiple instances: <lang Verilog> module Half_Adder( output c, s, input a, b );
xor xor01 (s, a, b); and and01 (c, a, b);
endmodule // Half_Adder
module Full_Adder( output c_out, s, input a, b, c_in );
wire s_ha1, c_ha1, c_ha2;
Half_Adder ha01( c_ha1, s_ha1, a, b ); Half_Adder ha02( c_ha2, s, s_ha1, c_in ); or or01 ( c_out, c_ha1, c_ha2 );
endmodule // Full_Adder
module Full_Adder4( output [4:0] s, input [3:0] a, b, input c_in );
wire [4:0] c;
Full_Adder adder00 ( c[1], s[0], a[0], b[0], c_in ); Full_Adder adder01 ( c[2], s[1], a[1], b[1], c[1] ); Full_Adder adder02 ( c[3], s[2], a[2], b[2], c[2] ); Full_Adder adder03 ( c[4], s[3], a[3], b[3], c[3] );
assign s[4] = c[4];
endmodule // Full_Adder4
module test_Full_Adder();
reg [3:0] a; reg [3:0] b; wire [4:0] s;
Full_Adder4 FA4 ( s, a, b, 0 );
initial begin
$display( " a + b = s" );
$monitor( "%4d + %4d = %5d", a, b, s );
a=4'b0000; b=4'b0000;
#1 a=4'b0000; b=4'b0001;
#1 a=4'b0001; b=4'b0001;
#1 a=4'b0011; b=4'b0001;
#1 a=4'b0111; b=4'b0001;
#1 a=4'b1111; b=4'b0001;
end
endmodule // test_Full_Adder </lang>
- Output:
a + b = s 0 + 0 = 0 0 + 1 = 1 1 + 1 = 2 3 + 1 = 4 7 + 1 = 8 15 + 1 = 16
VHDL
The following is a direct implementation of the proposed schematic: <lang VHDL>LIBRARY ieee; USE ieee.std_logic_1164.all;
entity four_bit_adder is
port(
a : in std_logic_vector (3 downto 0);
b : in std_logic_vector (3 downto 0);
s : out std_logic_vector (3 downto 0);
v : out std_logic
);
end four_bit_adder ;
LIBRARY ieee; USE ieee.std_logic_1164.all;
entity fa is
port(
a : in std_logic;
b : in std_logic;
ci : in std_logic;
co : out std_logic;
s : out std_logic
);
end fa ;
LIBRARY ieee; USE ieee.std_logic_1164.all;
entity ha is
port(
a : in std_logic;
b : in std_logic;
c : out std_logic;
s : out std_logic
);
end ha ;
LIBRARY ieee; USE ieee.std_logic_1164.all;
entity xor_gate is
port(
a : in std_logic;
b : in std_logic;
x : out std_logic
);
end xor_gate ;
architecture struct of four_bit_adder is
signal ci0 : std_logic; signal co0 : std_logic; signal co1 : std_logic; signal co2 : std_logic;
component fa
port (
a : in std_logic ;
b : in std_logic ;
ci : in std_logic ;
co : out std_logic ;
s : out std_logic
);
end component;
begin
ci0 <= '0';
i_fa0 : fa
port map (
a => a(0),
b => b(0),
ci => ci0,
co => co0,
s => s(0)
);
i_fa1 : fa
port map (
a => a(1),
b => b(1),
ci => co0,
co => co1,
s => s(1)
);
i_fa2 : fa
port map (
a => a(2),
b => b(2),
ci => co1,
co => co2,
s => s(2)
);
i_fa3 : fa
port map (
a => a(3),
b => b(3),
ci => co2,
co => v,
s => s(3)
);
end struct;
architecture struct of fa is
signal c1 : std_logic; signal c2 : std_logic; signal s1 : std_logic;
component ha
port (
a : in std_logic ;
b : in std_logic ;
c : out std_logic ;
s : out std_logic
);
end component;
begin
co <= c1 or c2;
i_ha0 : ha
port map (
a => ci,
b => a,
c => c1,
s => s1
);
i_ha1 : ha
port map (
a => s1,
b => b,
c => c2,
s => s
);
end struct;
architecture struct of ha is
component xor_gate
port (
a : in std_logic;
b : in std_logic;
x : out std_logic
);
end component;
begin
c <= a and b;
i_xor_gate : xor_gate
port map (
a => a,
b => b,
x => s
);
end struct;
architecture rtl of xor_gate is
begin
x <= (a and not b) or (b and not a);
end architecture rtl;</lang>
An exhaustive testbench:
<lang VHDL>LIBRARY ieee;
USE ieee.std_logic_1164.all;
use ieee.NUMERIC_STD.all;
entity tb is end tb ;
architecture struct of tb is
signal a : std_logic_vector(3 downto 0); signal b : std_logic_vector(3 downto 0); signal s : std_logic_vector(3 downto 0); signal v : std_logic;
component four_bit_adder
port (
a : in std_logic_vector (3 downto 0);
b : in std_logic_vector (3 downto 0);
s : out std_logic_vector (3 downto 0);
v : out std_logic
);
end component;
begin
proc_test: process
begin
for x in 0 to 15 loop
for y in 0 to 15 loop
a <= std_logic_vector(to_unsigned(x, 4));
b <= std_logic_vector(to_unsigned(y, 4));
wait for 100 ns;
end loop;
end loop;
wait;
end process;
i_four_bit_adder : four_bit_adder
port map (
a => a,
b => b,
s => s,
v => v
);
end struct;</lang>
XPL0
<lang XPL0>code CrLf=9, IntOut=11;
func Not(A); int A; return not A;
func And(A, B); int A, B; return A and B;
func Or(A, B); int A, B; return A or B;
func Xor(A, B); int A, B; return Or(And(A, Not(B)), And(Not(A), B));
proc HalfAdd(A, B, S, C); int A, B, S, C; [S(0):= Xor(A, B);
C(0):= And(A, B);
];
proc FullAdd(A, B, Ci, S, Co); int A, B, Ci, S, Co; \(Ci and Co are reversed from drawing) int S0, S1, C0, C1; [HalfAdd(Ci, A, @S0, @C0);
HalfAdd(S0, B, @S1, @C1); S(0):= S1; Co(0):= Or(C0, C1);
];
proc Add4Bits(A0, A1, A2, A3, B0, B1, B2, B3, S0, S1, S2, S3, Co); int A0, A1, A2, A3, B0, B1, B2, B3, S0, S1, S2, S3, Co; int Co0, Co1, Co2; [FullAdd(A0, B0, 0, S0, @Co0);
FullAdd(A1, B1, Co0, S1, @Co1); FullAdd(A2, B2, Co1, S2, @Co2); FullAdd(A3, B3, Co2, S3, Co);
];
proc BinOut(D, A0, A1, A2, A3, C); int D, A0, A1, A2, A3, C; [IntOut(D, C&1); IntOut(D, A3&1); IntOut(D, A2&1); IntOut(D, A1&1); IntOut(D, A0&1); ];
int S0, S1, S2, S3, C; [Add4Bits(1, 0, 0, 0, 0, 0, 1, 0, @S0, @S1, @S2, @S3, @C); \0001 + 0100 = 00101
BinOut(0, S0, S1, S2, S3, C); CrLf(0); Add4Bits(1, 0, 1, 0, 0, 1, 1, 1, @S0, @S1, @S2, @S3, @C); \0101 + 1110 = 10011 BinOut(0, S0, S1, S2, S3, C); CrLf(0); Add4Bits(1, 1, 1, 1, 1, 1, 1, 1, @S0, @S1, @S2, @S3, @C); \1111 + 1111 = 11110 BinOut(0, S0, S1, S2, S3, C); CrLf(0);
]</lang>
- Output:
00101 10011 11110
zkl
<lang zkl>fcn xor(a,b) // a,b are 1|0 -->a^b(1|0)
{ a.bitAnd(b.bitNot()).bitOr(b.bitAnd(a.bitNot())) }
fcn halfAdder(a,b) // -->(carry, a+b) (1|0)
{ return(a.bitAnd(b), xor(a,b)) }
fcn fullBitAdder(c, a,b){ //-->(carry, a+b+c), a,b,c are 1|0
c1,s := halfAdder(a,c); c2,s := halfAdder(s,b); c3 := c1.bitOr(c2); return(c3,s);
}
// big endian
fcn fourBitAdder(a3,a2,a1,a0, b3,b2,b1,b0){ //-->(carry, s3,s2,s1,s0)
c,s0 := fullBitAdder(0, a0,b0); c,s1 := fullBitAdder(c, a1,b1); c,s2 := fullBitAdder(c, a2,b2); c,s3 := fullBitAdder(c, a3,b3); return(c, s3,s2,s1,s0);
}
// add(10,9) result should be 1 0 0 1 1 (0x13, 3 carry 1) println(fourBitAdder(1,0,1,0, 1,0,0,1));</lang> <lang zkl>fcn nBitAddr(as,bs){ //-->(carry, sn..s3,s2,s1,s0)
(ss:=List()).append(
[as.len()-1 .. 0,-1].reduce('wrap(c,n){
c2,s:=fullBitAdder(c,as[n],bs[n]); ss + s; c2
},0))
.reverse();
} println(nBitAddr(T(1,0,1,0), T(1,0,0,1)));</lang>
- Output:
L(1,0,0,1,1) L(1,0,0,1,1)
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