The GATE Grind

GATE 2024 CS (CS1) – Question 47

Digital Logic · Boolean Algebra and Minimization · 2 marks · Multiple select

Consider a Boolean expression given by $F(X,Y,Z)=\sum(3,5,6,7)$. Which of the following statements is/are CORRECT?

  1. $F(X,Y,Z)=\Pi(0,1,2,4)$
  2. $F(X,Y,Z)=XY+YZ+XZ$
  3. $F(X,Y,Z)$ is independent of input $Y$
  4. $F(X,Y,Z)$ is independent of input $X$

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Show answer and explanation

Correct answer: (A) $F(X,Y,Z)=\Pi(0,1,2,4)$; (B) $F(X,Y,Z)=XY+YZ+XZ$

Explanation

Maxterms are the complement set {0,1,2,4}. Minimizing gives XY+YZ+XZ (majority function), which depends on all three inputs.