Consider the following min term expression for F. F (P, Q, R, S) = ∑ ( 0, 2, 5, 7, 8, 10, 13, 15 ) The min-terms 2, 7, 8 and 13 are ‘do not care’ terms. The minimal sum-of-products form for F is

The required minterms are 0, 5, 10, 15, and the don't cares are 2, 7, 8, 13. On the K-map: 0, 2, 8, 10 are the four corners. These are cells where Q = 0 and S = 0, giving the term \( Q S \). 5, 7, 13, 15 are the middle block, cells where Q = 1 and S = 1, giving the term \(QS\). So \(F = Q S + QS\). Answer: (B)

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Consider the following min term expression for F.

F (P, Q, R, S) =..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep."> Consider the following min... - Solved | MCA Prep" /> Consider the following min term expression for F.

F (P, Q, R, S) =..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." /> Consider the following min... - Solved | MCA Prep" /> Consider the following min term expression for F.

F (P, Q, R, S) =..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." />

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Question 95

Computer Awareness Boolean algebra Hard

<p style="">Consider the following min term expression for F.</p> <p style="">F (P, Q, R, S) = ∑  ( 0, 2, 5, 7, 8, 10, 13, 15 )</p> The min-terms 2, 7, 8 and 13 are ‘do not care’ terms. The minimal sum-of-products form for F is 

(A) QS̅ + Q̅ S 

(B) Q̅S̅ + QS

(C) Q̅R̅S̅ + Q̅RS̅+ QR̅S + QRS

(D) P̅Q̅S̅ + P̅QS + PQS + PQ̅S̅ 

✓ Correct Answer: Option B Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

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

On the K-map:

0, 2, 8, 10 are the four corners. These are cells where Q = 0 and S = 0, giving the term \(\bar{Q}\bar{S}\).
5, 7, 13, 15 are the middle block, cells where Q = 1 and S = 1, giving the term \(QS\).

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

Answer: (B)