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GATE CSE 2026 Session 2 Q59: Inputs giving Y = 1 for a decoder feeding a 4-to-1 MUX

Question

Consider the digital circuit shown below with two input lines A and B, two select lines S0 and S1, and an output line Y. The blocks Q and M represent active high 2:4 decoder and 4-to-1 multiplexer, respectively. Out of 16 possible input combinations, the number of combinations that produce Y=1 is ____________. (answer in integer)

Note: One input combination is an instance of [A B S1 S0].

A and B feed a 2:4 decoder Q; decoder output D0 goes to MUX input 0, constant 0 to input 1, constant 1 to input 2, and D3 to input 3 of a 4-to-1 MUX M with selects S1 and S0 and output Y
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Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 6 (official GATE 2026 final answer key)

Concept used: A 2:4 decoder makes exactly one output 1 (D0 = A′B′, D3 = AB); the MUX passes the input chosen by S1 S0.

First step: For each value of S1 S0, count how many (A, B) pairs make the selected MUX input equal to 1.

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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