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GATE CSE 2025 Session 1 Q42: Minimise F = Σ(0, 2, 4, 8, 10, 11, 12)

Question

Consider the following four variable Boolean function in sum-of-product form

F(b3,b2,b1,b0)=∑(0,2,4,8,10,11,12).F(b_3, b_2, b_1, b_0) = \sum(0, 2, 4, 8, 10, 11, 12).

where the value of the function is computed by considering b3b2b1b0b_3 b_2 b_1 b_0 as a 4-bit binary number, where b3b_3 denotes the most significant bit and b0b_0 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 FF?

Try it: multiple choice: exactly one correct option

Select one option
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Answer: A (official GATE 2025 final answer key)

Concept used: K-map minimisation: cover every minterm with the fewest, largest prime implicants.

First step: Minterms 0, 4, 8, 12 form b1‾ b0‾\overline{b_1}\,\overline{b_0} and 0, 2, 8, 10 form b2‾ b0‾\overline{b_2}\,\overline{b_0}; minterm 11 is left and pairs only with 10.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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