For a binary half-subtractor having two inputs A and B, the correct set of logical expression for the outputs D (= A minus B) and X (= borrow) are

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ISRO (VSSC) Technical Assistant Electrical 2017 Official Paper
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  1. \(D=AB+A\bar B,X=\bar AB\)
  2. \(D=A\bar B+A\bar B ,X=A\bar B\)
  3. \(D=A \bar B+\bar AB ,X=\bar AB\)
  4. \(D=AB+A \bar B,X=A\bar B\)

Answer (Detailed Solution Below)

Option 3 : \(D=A \bar B+\bar AB ,X=\bar AB\)
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Detailed Solution

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Truth Table for half substractor:

A B Difference Borrow
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0

 

\( Difference = A⊕B = A\bar B + \bar AB \)

\(Borrow = X=\bar AB\)

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