Consider the following minterm for F: \(... - Solved

Question 75

Computer Awareness Boolean algebra Easy

Consider the following minterm for F: \( \pi(P, Q, R, S) = \sum (0, 2, 5, 7, 8, 10, 13, 15) \). The minterms 2, 7, 8, and 13 are don't care terms. The minimal sum of products form for F is

(A) \(\overline{Q}S+Q\overline{S}\)

(B) \(\overline{Q}\, \overline{S}+QS\)

(C) \(\overline{Q}\, \overline{R}\, \overline{S}+\overline{Q}\, R\overline{S}+Q\overline{R}\, S+QRS\)

(D) \(\overline{P}\, \overline{Q}\, \overline{S}+\overline{P}\, QS+PQS+P\, \overline{Q}\, \overline{S}\)

✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The required minterms are 0, 5, 10, 15, with don't cares 2, 7, 8, 13.

{0, 2, 8, 10} (the four corners, where Q = 0 and S = 0) gives \(\bar{Q}\bar{S}\).
{5, 7, 13, 15} (where Q = 1 and S = 1) gives \(QS\).

\(F = \bar{Q}\bar{S} + QS\)

Answer: (B)

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Question 75

📘 Step-by-Step Solution & Detailed Explanation:

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