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GATE 2025 IN – Question 17

Digital Electronics · Number systems and combinational logic · 1 mark · Multiple choice

The minimized Boolean expression $Y(P,Q,R)$ implemented by the shown multiplexer circuit is

Diagram for GATE 2025 IN question 17
  1. $Y=R+(P\oplus Q)$
  2. $Y=R(P\oplus Q)$
  3. $Y=R+\overline{P\oplus Q}$
  4. $Y=R\oplus(P\oplus Q)$

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Show answer and explanation

Correct answer: (A) $Y=R+(P\oplus Q)$

Explanation

The first multiplexer outputs 0,1,1,0 for selectors 00,01,10,11, so it implements P XOR Q.

The second selects that result when R=0 and constant 1 when R=1.

Thus Y=Rbar(P XOR Q)+R=**R+(P XOR Q), A**.