The GATE Grind

GATE 2023 IN – Question 40

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

Simplify $F(W,X,Y,Z)=\Sigma(4,5,10,11,12,13,14,15)$ using the minimum number of terms and fewest literals per term.

  1. $WX+\bar W X\bar Y+W\bar X Y$
  2. $WX+WY+X\bar Y$
  3. $X\bar Y+WY$
  4. $\bar X Y+\bar W\bar Y$

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Show answer and explanation

Correct answer: (C) $X\bar Y+WY$

Explanation

Group minterms 4,5,12,13 to obtain $X\bar Y$ and 10,11,14,15 to obtain $WY$. Each group removes Z and one other variable. The minimal sum is $X\bar Y+WY$, **C**.