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GATE 2015 EE (EE2) – Question 48

Analog and Digital Electronics · VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers · 2 marks · Multiple choice

Implement $f(A,B,C,D)=\Pi(1,5,12,15)$ using an 8:1 MUX. A is MSB and ABC drive S2,S1,S0. Which ordered pin inputs 0–7 are correct?

Diagram for GATE 2015 EE (EE2) question 48
  1. $D,0,D,0,0,0,\bar D,D$
  2. $\bar D,1,\bar D,1,1,1,D,\bar D$
  3. $D,1,D,1,1,1,\bar D,D$
  4. $\bar D,0,\bar D,0,0,0,D,\bar D$

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Show answer and explanation

Correct answer: (B) $\bar D,1,\bar D,1,1,1,D,\bar D$

Explanation

The Π notation lists zero indices. For each fixed ABC, compare the two values at D=0 and D=1.

Pin 0 covers indices 0,1 and gives D̄. Pin 2 covers 4,5 and also gives D̄. Pin 6 covers 12,13 and gives D. Pin 7 covers 14,15 and gives D̄. All remaining index pairs contain no zero and give constant 1.

Thus the ordered inputs are **D̄,1,D̄,1,1,1,D,D̄, B**.

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