GATE CS 2025 Set 1 — Question 42
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Digital Logic → Boolean Algebra & Logic Gates → K-Map Minimization
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Question
Consider the following four variable Boolean function in sum-of-product formwhere the value of the function is computed by considering as a 4-bit binary number, where denotes the most significant bit and denotes the least significant bit. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for ?
Correct answer
(A) b₁ b₀ + b₂ b₀ + b₁ b₂ b₃
Solution
To find the minimized Boolean expression for , we can use a Karnaugh map (K-map).The minterms are:
Grouping:
| 00 | 01 | 11 | 10 | |
|---|---|---|---|---|
| 00 | 1 (0) | 0 | 0 | 1 (2) |
| 01 | 1 (4) | 0 | 0 | 0 |
| 11 | 1 (12) | 0 | 0 | 0 |
| 10 | 1 (8) | 0 | 1 (11) | 1 (10) |
1.Quad 1 (Corners and edges): Minterms (0, 2, 8, 10). This group is formed by the cells where and . The term is .
2.Quad 2 (Column 00): Minterms (0, 4, 12, 8). This group is formed by the cells where and . The term is .
3.Pair: Minterms (10, 11). This group is formed by the cells where . The term is .
Combining these terms, the minimized expression is:This matches option (A).Continue learning with Success Tracker
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