Binary coded decimal

Binary coded decimal is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Binary-Coded Decimal (or BCD for short) is a method of representing decimal numbers by storing what appears to be a decimal number but is actually stored as hexadecimal. Many CISC CPUs (e.g. X86 Assembly have special hardware routines for displaying these kinds of numbers.) On low-level hardware, such as 7-segment displays, binary-coded decimal is very important for outputting data in a format the end user can understand.

Task

Use your language's built-in BCD functions, OR create your own conversion function, that converts an addition of hexadecimal numbers to binary-coded decimal. You should get the following results with these test cases:

•   0x19 + 1 = 0x20
•   0x30 - 1 = 0x29
•   0x99 + 1 = 0x100

Bonus Points

Demonstrate the above test cases in both "packed BCD" (two digits per byte) and "unpacked BCD" (one digit per byte).

68000 Assembly

The 68000 has special mathematics commands for binary-coded decimal. However, they only work at byte length, and cannot use immediate operands. Even adding by 1 this way requires you to load 1 into a register first. <lang 68000devpac> MOVEQ #$19,D0 MOVEQ #1,D1 MOVEQ #0,D2

ABCD D1,D0 JSR PrintHex JSR NewLine

MOVEQ #$30,D0 SBCD D1,D0 JSR PrintHex JSR NewLine

MOVE.B #$99,D0 ABCD D1,D0 ;D0 has rolled over to 00 and set both the extend and carry flags. ADDX D2,D2 ;add the extend flag which was set by the above operation ;this can't use immediate operands either so we're using D2 which we set to zero at the start.

MOVE.L D0,D3 ;back up the output since PrintHex takes D0 as its argument. MOVE.L D2,D0 ;print the 01 JSR PrintHex MOVE.L D3,D0 ;then the 00 JSR PrintHex

       jmp *</lang>

Output:

20
29
0100

Z80 Assembly

The DAA function will convert an 8-bit hexadecimal value to BCD after an addition or subtraction is performed. The algorithm used is actually quite complex, but the Z80's dedicated hardware for it makes it all happen in 4 clock cycles, tied with the fastest instructions the CPU can perform.

<lang z80> PrintChar equ &BB5A ;Amstrad CPC kernel's print routine org &1000

ld a,&19 add 1 daa call ShowHex call NewLine

ld a,&30 sub 1 daa call ShowHex call NewLine

ld a,&99 add 1 daa

this rolls over to 00 since DAA only works with the accumulator.

But the carry is set by this operation, so we can work accordingly.

jr nc,continue ;this branch is never taken, it exists to demonstrate the concept of how DAA affects the carry flag. push af ld a,1 call ShowHex pop af continue: call ShowHex call NewLine ret ;return to basic

ShowHex: push af and %11110000 rrca rrca rrca rrca call PrintHexChar pop af and %00001111 ;call PrintHexChar ;execution flows into it naturally. PrintHexChar: ;this little trick converts hexadecimal or BCD to ASCII. or a ;Clear Carry Flag daa add a,&F0 adc a,&40 jp PrintChar</lang>

Output:

20
29
0100