Question

The diagram of a logic circuit is given below. The output $F$ of the circuit is given by

• A. $W.(X+Y)$
• B. $W.(X.Y)$
• C. $W+(X.Y)$
• D. $W+(X+Y)$

Answer 1

The correct option is D $W+(X+Y)$

The outputs from first $\text{NOR}$ gates will act as inputs for $\text{NAND}$ gate as shown,


Thus, the output $F$ is given by,

$F=\overline{\left(\overline{W+X}\right).\left(\overline{W+Y}\right)}$

Applying DeMorgan's theorem,

$\left(\overline{A.B}\right)=\overline{A}+\overline{B}$

$\Rightarrow F=(\overline{\overline{W+X})}+\overline{\left(\overline{W+Y}\right)}$

$\Rightarrow F=(W+X)+(W+Y)$

$\Rightarrow F=(W+W)+(X+Y)$

As, $[W+W=W]$

$\therefore F=W+(X+Y)$

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