Find the minimal sum-of-products form of F(P,Q,R,S)=PQ+ PQR+ PQ RS.

GATE 2014 CS (CS1) – Question 17

Digital Logic · Boolean Algebra and Minimization · 1 mark · Multiple choice

Find the minimal sum-of-products form of $F(P,Q,R,S)=PQ+\bar PQR+\bar PQ\bar RS$.

$PQ+QR+QS$
$P+Q+R+S$
$\bar P+\bar Q+\bar R+\bar S$
$\bar PR+\bar P\bar RS+P$

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Correct answer: (A) $PQ+QR+QS$

Explanation

Use P+P̄X=P+X within PQ+P̄QR to obtain PQ+QR. Then QR+Q R̄S=Q(R+S)=QR+QS, with the existing PQ allowing the remaining P̄ restriction to be removed by absorption. The minimal result is **PQ+QR+QS, A**.