Question

Consider the 4 to 1 multiplexer with two select line $S_1$ and $S_0$ given below.


The minimal sum of products form of the Boolean expression for the output F of the multiplexer is

• A. $\overline{P}QR+\overline{Q}\overline{R}+QP$
• B. $\overline{P}QR+Q\overline{P}+\overline{Q}\overline{R}$
• C. $P\overline{Q}R+\overline{Q}\overline{R}+\overline{Q}P$
• D. $\overline{Q}\overline{R}+\overline{Q}P+P\overline{Q}R$

Answer 1

The correct option is D

$\overline{Q}\overline{R}+\overline{Q}P+P\overline{Q}R$

$\begin{array}{c}\\ F=\overline{P}QR+\overline{Q}\overline{R}+QP\\ =\overline{P}QR+Q\overline{P}+\overline{Q}\overline{R}\\ =P\overline{Q}R+\overline{Q}\overline{R}+\overline{Q}P\\ =\overline{Q}\overline{R}+\overline{Q}P+\overline{P}QR\end{array}$