MCQ
What will be the input of $A$ and $B$ for the Boolean expression $\overline {(A + B)} \, \cdot \,\overline {(A \cdot B)} = 1$
- ✓$0, 0$
- B$0, 1$
- C$1, 0$
- D$1, 1$
✓
Answer
Correct option: A.
$0, 0$
a
(a)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)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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