Semiconducting Devices Question 79

Question: What will be the input of A and B for the Boolean expression $ \overline{(A+B)}\cdot \overline{(A\cdot B)}=1 $

[TNPCEE 2002]

Options:

A) 0, 0

B) 0, 1

C) 1, 0

D) 1, 1

Show Answer

Answer:

Correct Answer: A

Solution:

The given Boolean expression can be written as $ Y=(\overline{A+B}).(\overline{A.B})=(\bar{A}.\bar{B}).(\bar{A}+\bar{B})=(\bar{A}\bar{A}).\bar{B}+\bar{A}(\bar{B}.\bar{B}) $

$ =\bar{A}.\bar{B}+\bar{A}\bar{B}=\bar{A}\bar{B} $

A B Y
0 0 1
1 0 0
0 1 0
1 1 0


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