What would be the value of register AL after the execution of the following assembly language program of 8086 ? AL = 53, CL = 29
ADD AL, CL
DAA
82
The two instructions perform a packed-BCD addition: 53 plus 29 in decimal is 82, and DAA is what makes the binary hardware produce that answer.
Step 1 — the binary addition. The values are packed BCD, so each nibble holds one decimal digit.
\(53_{H}+29_{H}=7C_{H}\)
Checking nibble by nibble: \(3+9=12=C_{H}\) in the low nibble with no carry out, and \(5+2=7\) in the high nibble. The processor has done ordinary binary arithmetic and produced 7C — which is not valid BCD, since C is not a decimal digit. This is why option 1 is offered: it is the answer before the adjustment.
Step 2 — what DAA does with it. The rule is applied to each nibble in turn:
| Test | Action | Here |
|---|---|---|
| Low nibble > 9, or AF = 1 | Add 06H, set AF | C > 9, so add 06 |
| High nibble > 9, or CF = 1 | Add 60H, set CF | 8 is not > 9, no CF — no action |
\(7C_{H}+06_{H}=82_{H}\)
The high nibble is now 8, which is a legal digit and no greater than 9, so the second rule does not fire. AL = 82H — option 2, reading directly as the decimal answer 82.
Why adding 6 is the right correction. A nibble counts in sixteens but a decimal digit counts in tens, so whenever a digit sum passes 9 the binary result is short of a decimal carry by exactly \(16-10=6\). Adding 6 pushes the nibble past 16, which both generates the carry into the next digit and leaves the correct remainder behind. Here \(C+6=12_{H}\) gives a carry of 1 into the high nibble and a 2 left in the low nibble — exactly the decimal digits of 82.
Why the other options are wrong. Option 3, DC, would follow from adding 60H instead of 06H — adjusting the wrong nibble. Option 4, E8, comes from adding 66H, applying both corrections when only one was needed.
The point of packed BCD is that the digits can be read out directly for a display or printed record without any binary-to-decimal conversion, which is why it survives in calculators, tills and real-time clock chips.
Hence, AL = 82.
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