GATE CS 2026 Set 1 — Question 48
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
Consider a Boolean function with the following minterm expression:Which of the following options is/are the minimal sum-of-products expression(s) of ?
Correct answer
(B) PS + QR + PQR + PRS; (D) PS + QR + PQS + QRS
Solution
We map the minterms to a K-map:
Prime Implicants:
We need to cover m2 (0010), m10 (1010), and m14 (1110).Option 1 (Matches D):
| 00 | 01 | 11 | 10 | |
|---|---|---|---|---|
| 00 | 0 | 1 (m1) | 1 (m3) | 1 (m2) |
| 01 | 1 (m4) | 1 (m5) | 1 (m7) | 0 |
| 11 | 1 (m12) | 1 (m13) | 0 | 1 (m14) |
| 10 | 0 | 0 | 0 | 1 (m10) |
1.Essential: Quad (1, 3, 5, 7)
2.Essential: Quad (4, 5, 12, 13)
Remaining minterms to cover: m2, m10, m14.Covering remaining minterms:We need to cover m2 (0010), m10 (1010), and m14 (1110).Option 1 (Matches D):
- Group (2, 10)
- Group (12, 14)
- Group (2, 3)
- Group (10, 14)
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