Given the following Karnaugh Map for F(w,x,y,z): yz: 00 01 11 10
wx=00: 1 0 0 1
wx=01:

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GATE-CS is a competitive examination conducted in India. This question is from the 2025 GATE-CS Digital Logic paper.

Q: How can I prepare for GATE-CS Digital Logic?

To prepare for GATE-CS Digital Logic, practice previous year questions (PYQs), understand concepts thoroughly, and solve mock tests regularly. This 2025 question covers Minimization (K-Map, Quine-McCluskey) topic.

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This GATE-CS 2025 Digital Logic question has a hard difficulty level and is marked as an important question.

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Question

Given the following Karnaugh Map for F(w,x,y,z):      yz: 00 01 11 10
wx=00:     1  0  0  1
wx=01:     0  1  1  0
wx=11:     0  1  1  0
wx=10:     1  0  0  1Which Boolean expression(s) represent F?

Accepted Answer

Correct Answer: (A) and (D)K-Map Analysis (minterms at 1): Minterms: 0(0000), 2(0010), 5(0101), 7(0111), 8(1000), 10(1010), 13(1101), 15(1111).Pattern: F = 1 when (x=0,z=0) OR (x=1,z=1) → F = x̄z̄ + xz (XNOR of x and z). Option D is correct.Option A: xz covers {5,7,13,15}. The remaining terms wxyz(=m15), w̄x̄ȳz̄(=m0), w̄xyz(=m7) add redundant but valid product terms. Expanding and simplifying Option A yields the same truth table as F = x̄z̄ + xz. Option A is also correct.Option B: Contains xz̄ (covers minterms where x=1,z=0: m8,m10,m12,m14) — these include non-minterms like m12,m14. Incorrect.Option C: w̄x̄yz (minterm 6 = 0110) is not in the minterm list. Incorrect.

Given the following Karnaugh Map for F(w,x,y,z): yz: 00 01 11 10 wx=00: 1 0 0 1 wx=01: 0 1 1 0 wx=11: 0 1 1 0 wx=10: 1 0 0 1Which Boolean expression(s) represent F?

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Given the following Karnaugh Map for F(w,x,y,z): yz: 00 01 11 10 wx=00: 1 0 0 1 wx=01: 0 1 1 0 wx=11: 0 1 1 0 wx=10: 1 0 0 1Which Boolean expression(s) represent F?

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More Questions from Minimization (K-Map, Quine-McCluskey)

Frequently Asked Questions