The GATE Grind

GATE 2023 CS – Question 44

Digital Logic · Combinational Circuits · 2 marks · Multiple choice

A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0–X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown (M1 and M2 use A as S1 and C as S0; M3 uses B as select, with M1 on input 0 and M2 on input 1). Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7) will realise the Boolean function $\bar{A} + \bar{A}C + ABC$?

Diagram for GATE 2023 CS question 44
  1. (1, 1, 0, 0, 1, 1, 1, 0)
  2. (1, 1, 0, 0, 1, 1, 0, 1)
  3. (1, 1, 0, 1, 1, 1, 0, 0)
  4. (0, 0, 1, 1, 0, 1, 1, 1)

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) (1, 1, 0, 0, 1, 1, 0, 1)

Explanation

The function simplifies to Ā + BC. For B=0 it is Ā, so (X0..X3) = 1,1,0,0. For B=1 it is Ā + C, so for AC=00,01,10,11 the values are 1,1,0,1, giving (X4..X7) = 1,1,0,1.