Consider the following Boolean expression for \(F\): \(F(P,Q,R,S)= PQ +…
2014
Consider the following Boolean expression for \(F\):
\(F(P,Q,R,S)= PQ + \bar{P}QR + \bar{P}Q\bar{R}S\)
The minimal sum-of-products form of \(F\) is
- A.
\(PQ+QR+QS\) - B.
\(P+Q+R+S\) - C.
\(\bar{P} + \bar{Q}+ \bar{R}+ \bar{S}\) - D.
\(\bar{P}R + \bar{R} \bar{P}S+P\)
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Correct answer: A
Key insight: all terms contain Q, so factor Q.
Start: F = PQ + P'QR + P'Q R' S
Factor Q: F = Q(P + P'R + P'R'S)
Use the identity X + X'Y = X + Y with X = P and Y = R + S:
P + P'(R + R'S) = P + P'(R + S) = P + R + S
Therefore F = Q(P + R + S) = PQ + QR + QS, which is the minimal sum-of-products form.
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