Question

The output $Y$ of the logic circuit given above is:

• A. $\overline{A}+B$
• B. $\overline{A}$
• C. $\overline{(\overline{A}+B)}\cdot \overline{A}$
• D. $\overline{(\overline{A}+B)}\cdot A$

Answer 1

Answer: (B)

$\overline{A}$

Using the Boolean expression, we write the output for each logic gate as shown.

The output of signal $A$ after passing through $NOT$ gate is $\overline{A}$

The output of signals $\overline{A}$ and $B$ after passing through $AND$ gate is $\overline{A}.B$

The output of signals $\overline{A}.B$ and $\overline{A}$ after passing through $OR$ gate is $\overline{A}+\overline{A}.B$

Thus the output signal of the logic circuit $Y=\overline{A}+\overline{A}.B$

$\therefore$ $Y=\overline{A}(1+B)$

Using $1+B=1$ , we get $Y=\overline{A}.1$

$⟹Y=\overline{A}$