Consider the following 4-variable Boolean function:F(A, B, C, D) = Sigma_m(0, 1, 2, 3, 8, 9, 10, 11)

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GATE-CS is a competitive examination conducted in India. This question is from the 2026 GATE-CS Digital Logic paper.

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This GATE-CS 2026 Digital Logic question has a medium difficulty level and is marked as an important question.

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Question

Consider the following 4-variable Boolean function:F(A, B, C, D) = Sigma_m(0, 1, 2, 3, 8, 9, 10, 11)Consider A as MSB, D as LSB. Which one of the following options represents the minimal sum of products form for the above function?Note: + is OR, . is AND, ' is NOT

Accepted Answer

Correct Answer: (B) B'Concept -- Karnaugh Map Minimization: Minterms: 0,1,2,3 (binary 0000,0001,0010,0011) → A=0, B=0; minterms 8,9,10,11 (1000,1001,1010,1011) → A=1, B=0. All minterms have B=0. The K-map grouping of 8 cells (two groups of 4) yields the single literal B' (B complement). Minimal SOP = B'.Why other options are incorrect: • A – A'+B'+C'+D' would cover many more minterms (all except 15 maybe), not minimal and includes unnecessary literals.• C – A'B' + AB would cover minterms with A=B=0 and A=B=1, but our minterms have B=0 only, and A'B' covers 0-3, AB covers 8-11? Actually AB means A=1,B=1, which would give minterms 12-15, not in the set. So C is wrong.• D – A' would cover minterms 0-7 (A=0), but we also have minterms 8-11 (A=1), so A' alone is insufficient.Note: K-map simplification for 4 variables: groups of 1,2,4,8,16 cells. Here we have two groups of 4 that combine to a group of 8 cells covering all minterms with B=0, yielding B'.

Consider the following 4-variable Boolean function:F(A, B, C, D) = Sigma_m(0, 1, 2, 3, 8, 9, 10, 11)Consider A as MSB, D as LSB. Which one of the following options represents the minimal sum of products form for the above function?Note: + is OR, . is AND, ' is NOT

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Consider the following 4-variable Boolean function:F(A, B, C, D) = Sigma_m(0, 1, 2, 3, 8, 9, 10, 11)Consider A as MSB, D as LSB. Which one of the following options represents the minimal sum of products form for the above function?Note: + is OR, . is AND, ' is NOT

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