BCD Subtraction via Ten's Complement
BCD arithmetic units unify addition and subtraction logic by leveraging ten's complement, mirroring the two's complement approach used in standard binary ALUs.
The operation 47 - 29 must be executed using ten's complement addition in BCD format. The subtrahend 29 is first converted to its nine's complement, then incremented by 1 to form the ten's complement. This value is added to the minuend 47 using standard BCD addition rules.
Trace the intermediate values during the complement generation, execute the raw binary addition, apply any necessary BCD corrections, and determine the final valid BCD output.
Constraints
- All intermediate additions must follow strict binary and BCD rules.
- Correction involves adding
0110(6) to any decade exceeding1001(9) or generating a carry out to the next higher nibble. - The system is limited to two BCD digits. Any carry out of the most significant digit is an end carry.
Topics
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