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GATE 2021 IN – Question 45

Digital Electronics · Number systems and combinational logic · 2 marks · Multiple choice

A 4×1 MUX realizes Boolean $F(X,Y,Z,W)$. $S_0$ is the LSB and $S_1$ the MSB selector, connected as shown. $I_0$–$I_3$ are its inputs. Its canonical sum-of-products representation is ______.

Diagram for GATE 2021 IN question 45
  1. $\Sigma m(0,1,3,14,15)$
  2. $\Sigma m(0,1,3,11,14)$
  3. $\Sigma m(2,5,9,11,14)$
  4. $\Sigma m(1,3,7,9,15)$

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Show answer and explanation

Correct answer: (B) $\Sigma m(0,1,3,11,14)$

Explanation

Selectors XY=00 choose Z′+W, giving ZW=00,01,11 and minterms 0,1,3. XY=01 selects zero. XY=10 chooses ZW and gives minterm 11. XY=11 chooses ZW′ and gives minterm 14.

Therefore **Σm(0,1,3,11,14), B**, using X as MSB and W as LSB.