GATE ECE 2016 Set 3 | Question: 43

Question

Following is the K-map of a Boolean function of five variables $P,Q,R,S$ and $X$. The minimum sum-of-product (SOP) expression for the function is

• A. $\overline{P}\:\overline{Q}\:S\:\overline{X}+\;P\:\overline{Q}\:S\:\overline{X}+\;Q\:\overline{R}\:\overline{S}\:X+\;Q\:R\:\overline{S}\:X$
• B. $\overline{Q}\:S\:\overline{X}+\;Q\:\overline{S}\:X$
• C. $\overline{Q}\:S\:X+\;Q\:\overline{S}\:\overline{X}$
• D. $\overline{Q}\:S+\;Q\overline{S}$

Answer 1

The given boolean function $f(P,Q,R,S,X)$ has the following behavior:

When $X = 0,$ $f = Q’S$

When $X = 1, f = QS’$

So, we can write expression for $f$ as following: $f = X’ Q’S + X Q S’$

We can’t simplify it further. So, answer is Option B.