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GATE CSE 2024 Session 1 Q64: Select-line combinations giving Y = 1 in a tree of 2-to-1 MUXes

Question

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are select lines of M1, M2, and M3, respectively.

M1 has inputs X1 (0) and X2 (1), select S1 = A, output Q1. M2 has inputs X3 (0) and X4 (1), select S2 = B, output Q2. M3 takes Q1 on input 0 and Q2 on input 1, select S3 = C, output Y
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For an instance of inputs X1=1, X2=1, X3=0, and X4=0, the number of combinations of A, B, C that give the output Y=1 is _________

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 4 (official GATE 2024 final answer key)

Concept used: A 2-to-1 multiplexer passes input 0 when its select is 0 and input 1 when it is 1.

First step: Here Q1 = 1 whatever A is, and Q2 = 0 whatever B is; so Y depends only on C.

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Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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