GATE EC 2025 Set 1 — Question 23
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Digital Circuits → Combinational Logic → Boolean Algebra & Identities
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Question
A 3-input majority logic gate has inputs , , and . The output of the gate is logic ‘1’ if two or more of the inputs are logic ‘1’. The output is logic ‘0’ if two or more of the inputs are logic ‘0’. Which one of the following options is a Boolean expression of the output ?
Correct answer
(A) XY + YZ + ZX
Solution
A majority gate with 3 inputs produces a logic '1' output when at least two of its inputs are '1'. The possible combinations of inputs that result in are and .
The Boolean expression for is:
Using Boolean simplification:
Alternatively, by adding redundant terms:
Thus, the correct option is (A).
The Boolean expression for is:
Using Boolean simplification:
Alternatively, by adding redundant terms:
Thus, the correct option is (A).
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