Consider the Boolean function z(a, b, c). Which one of the following minterm lists represents the circuit given above?
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GATE CSE 2020 · Q28
Time

Select one answerSingle correct
Solution
Official answer: B) z = Σ (1, 4, 5, 6, 7)
Boolean Algebra and MinimizationFrom the given logic circuit diagram:
The NOT gate inverts input to .
The AND gate takes and as inputs, producing the term .
The OR gate takes input and the output of the AND gate , producing:
Now find the minterms corresponding to :
For the term (, with ): minterms are .
For the term (, with ): minterms are .
Taking the union of all minterms:
Hence, option B is the correct answer.
Try the question first, then check your work.
Examiner trap
Write the Boolean expression at the output of the OR gate in terms of , then expand it into sum of minterms.
This Boolean Algebra and Minimization previous year question is Q28 of the GATE CSE 2020 paper. Find more GATE CSE PYQs on Boolean Algebra and Minimization in Digital Logic, or browse all GATE CSE PYQs.
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Boolean Algebra and Minimization has 36 GATE CSE PYQs across 23 papers from 2011 to 2026. 9 of them are 2-mark MCQs like this one, and it is the only one in GATE CSE 2020.
How GATE tests Boolean Algebra and MinimizationIndependent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.