BCD Addition with Carry Correction
Hardware often interfaces directly with decimal displays where binary-coded decimal (BCD) simplifies the decoding logic. The system performs addition on two 4-bit BCD digits, A and B, producing a initial 4-bit binary sum S and a carry-out C_out. Because a 4-bit binary adder natively wraps at 16 while BCD wraps at 10, invalid states emerge when the sum exceeds 9.
Analyze the conditions under which a correction factor must be applied to the binary sum. Determine the corrected BCD sum for specific input combinations and identify the logic required to trigger the correction.
Constraints
- Inputs
AandBare guaranteed to be valid BCD digits (0 through 9). - The initial addition is performed by a standard 4-bit binary adder.
- The bits of the initial sum are denoted as
S3,S2,S1, andS0, whereS3is the most significant bit.
Topics
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