Project ForgeDigital Logic
Boolean Algebra & Minimization
GATE 2014
Hard
Consider the following Boolean expression for F:
F(P,Q,R,S) = PQ + P'QR + P'QR'S
The minimal sum-of-products form of F is
- PQ + QR + QS
- BP + Q + R + S
- CP' + Q' + R' + S'
- DP'R + P'RS + P
Explanation
Factor Q from the last two terms: P'QR + P'QR'S = P'Q(R + R'S) = P'Q(R+S) [since R+R'S=R+S]. So F = PQ + P'Q(R+S) = Q(P + P'(R+S)) = Q(P + R + S) [since A+A'B=A+B]. Distributing: F = PQ + QR + QS.
Source: GATE CS 2014 (Session 1) (2014)
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