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GATE 2024 EE – Question 26

Analog and Digital Electronics · VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers · 1 mark · Multiple choice

To obtain the Boolean function $F(X,Y)=X\bar Y+\bar X$, the inputs $PQRS$ in the figure should be

(4:1 multiplexer with inputs $P,Q,R,S$ on lines 0,1,2,3; select lines $S_1=X$ (MSB), $S_0=Y$.)

Diagram for GATE 2024 EE question 26
  1. 1010
  2. 1110
  3. 0110
  4. 0001

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Show answer and explanation

Correct answer: (B) 1110

Explanation

The multiplexer output equals the input selected by $XY$. Evaluate $F=X\bar Y+\bar X$: for $XY=00$, $F=1$ (so $P=1$); $XY=01$: $F=1$ ($Q=1$); $XY=10$: $F=1$ ($R=1$); $XY=11$: $F=0$ ($S=0$). So $PQRS=1110$.