Question

The output $\left(X\right)$ of the logic circuit shown in the figure will be-

• A. $X=\overline{A+B}$
• B. $X=\overline{\overline{A}}\cdot \overline{\overline{B}}$
• C. $X=\overline{A\cdot B}$
• D. $X=A\cdot B$

Answer 1

The correct option is D $X=A\cdot B$


The truth table for the above circuit is illustrated below.


Considering the inputs $A\text{and}B$ and the output $X$, the above truth table is that of an AND gate. So the output $X$ and the inputs $A\text{and}B$ are related as,
$X=A\cdot B$

Hence, $\left(D\right)$ is the correct answer.

Alternative method:

Since two NAND gates are connected one after the other, the output of the circuit will be,

$X=\overline{\overline{A\cdot B}}=A\cdot B$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.