Decimal Addition
Each 4 bit data quantity may be treated as a decimal number as long as it represents one of the decimal digits from 0 through 9, and does not contain any of the bit patterns representing the hexadecimal digits A through F.
In order to preserve this decimal interpretation when perfonning addition, the value 6 must be added to the accumulator whenever an addition produces a result between 10 and 15. This is because each 4 bit data quantity can hold 6 more combinations of bits than there are decimal digits.
The DAA (decimal adjust accumulator) instruction is provided for this purpose. Also, to permit addition of multi-digit decimal numbers, the DAA adds 6 to the accumulator whenever the carry bit is set indicating a decimal carry from previous additions. The carry bit is unaffected unless the addition of 6 produces a carry, in which case the carry bit is set.
Example: Perform the decimal addition
4 6 9
3 2 9 +
---
7 9 8
1 Clear the carry and add the lowest-order digits
9 = 1 0 0 1
9 = 1 0 0 1
Carry = 0
---------
Result 0 0 1 0
Carry 1
2 Perform a DAA operation, which will add 6 to the accumulator. Since no carry is produced by this operation, the carry bit is left unaffected (i.e. 1)
Accumulator = 0 0 1 0
6 = 0 1 1 0
Carry = 0
---------
Result 1 0 0 0 = 8
Carry 1
(since the DAA produced no carry, the bit is unaffected)
3 Add the next two digits
6 = 0 1 1 0
2 = 0 0 1 0
Carry = 1
---------
Result 1 0 0 1 = 9
Carry 0
4 Perform a DAA operation. Since the accumulator is not greater than 9, and the carry is not set, then no action occurs.
5 Add the next two digits
4 = 0 1 0 0
3 = 0 0 1 1
Carry = 0
---------
Result 0 1 1 1 = 7
Carry 0
6 Perform a DAA operation. Again, no action occurs. Thus, the correct result (798) is generated in three 4-bit data characters.
Example Code (subroutine)
A subroutine which adds two 16 digit decimal numbers can be found here:
