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For a binary half-subtractor having two inputs $\text{A}$ and $\text{B}$, the correct set of logical outputs $\text{D}\;(=\text{A}\;\text{minus} \;\text{B})$ and $\text{X}(=\text{borrow})$ are

  1. $\text{D}=\text{AB}+\overline{A}\text{B, X}=\overline{\text{A}}\text{B}$
  2. $\text{D}=\overline{A}\text{B}+A\overline{\text{B}}, \text{X = A}\overline{\text{B}}$
  3. $\text{D}=\overline{A}\text{B}+A\overline{\text{B}}, \text{X}=\overline{\text{A}} \text{B}$
  4. $\text{D}=\text{AB}+\overline{A}\text{B}, \text{X = A}\overline{\text{B}}$
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Best answer
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Truth table of half subtractor

A B D(A-B) X(Borrow)
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0

 Now check the values of  A and B for which D and X are 1

 D=A'B+AB'   or A⊕B  

X=A'B 

So ans is (C) D=A'B+AB'  , X=A'B 

edited by
1 votes
1 votes
For Half subtractor

Difference D = AB' +A'B

Borrow X= A'B

Hence C is correct.
Answer:

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