ISRO2016-9

Question

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

• A. $\text{D}=\text{AB}+\overline{A}\text{B, X}=\overline{\text{A}}\text{B}$
• B. $\text{D}=\overline{A}\text{B}+A\overline{\text{B}}, \text{X = A}\overline{\text{B}}$
• C. $\text{D}=\overline{A}\text{B}+A\overline{\text{B}}, \text{X}=\overline{\text{A}} \text{B}$
• D. $\text{D}=\text{AB}+\overline{A}\text{B}, \text{X = A}\overline{\text{B}}$

Answer 1

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 

Answer 2

For Half subtractor

Difference D = AB' +A'B

Borrow X= A'B

Hence C is correct.