For a binary half-subtractor having two inputs A and B, the correct set of…
2016
For a binary half-subtractor having two inputs A and B, the correct set of logical expressions for the outputs D (= A minus B) and X (=borrow) are
- A.
D = AB + A'B , X = A'B
- B.
D = A'B + AB' , X = AB'
- C.
D = A'B + AB' , X = A'B
- D.
D = AB + A'B , X = AB'
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Correct answer: C
A binary half-subtractor computes the difference (D) and borrow (X) for two single-bit inputs A and B. The truth table reveals that the difference D is 1 when A differs from B, which corresponds to the XOR operation: D = A'B + AB'. The borrow X is 1 only when A=0 and B=1, resulting in the expression X = A'B. Therefore, the correct logical expressions are D = A ⊕ B and X = A'B.
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