Question 81
Computer Awareness
Central Processing Unit (CPU)
Easy
Cosider the following Boolean Expression for F:\[F(P,Q,R,S)=PQ+\overline{P}QR+\overline{P}Q\overline{R}S\] The minimum sum of products form of F is
(A) \(PQ+QR+QS\)
(B) \(P+Q+R+S\)
(C) \(\overline{P}+\overline{Q}+\overline{R}+\overline{S}\)
(D) \(\overline{P}\, R+\, \overline{P}\, \overline{R}\, S+P\)
View Dynamic Solution & Explanation ▼
Correct Solution: Option A
Step-by-step Solution:
\[ \begin{array}{l} PQ + \overline{PQR} + \overline{PQRS} \\ = PQ + \overline{PQ}(R + RS) \\ = PQ + \overline{PQ} \left((R + R)(R + S)\right) \quad \text{(as we know } A + BC = (A + B)(A + C) \text{)} \\ = PQ + \overline{PQ} (R + S) \quad \text{(as we know } R + \overline{R} = 1 \text{)} \\ = Q(P + \overline{P}(R + S)) \quad \text{(Taking Q as common)} \\ = Q((P + \overline{P})(P + R + S)) \quad \text{(as we know } A + BC = (A + B)(A + C) \text{)} \\ = Q(P + R + S) \\ = PQ + QR + QS \\ = \text{Option A is correct} \end{array} \]
