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GATE 2020 CS – Question 38

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

Consider the Boolean function $z(a,b,c)$. [Figure: $z$ is the output of an OR gate whose inputs are $a$ and the output of an AND gate with inputs $\bar{b}$ (b passed through a NOT gate) and $c$]

Which one of the following minterm lists represents the circuit given above?

Diagram for GATE 2020 CS question 38
  1. $z=\sum(0,1,3,7)$
  2. $z=\sum(1,4,5,6,7)$
  3. $z=\sum(2,4,5,6,7)$
  4. $z=\sum(2,3,5)$

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Show answer and explanation

Correct answer: (B) $z=\sum(1,4,5,6,7)$

Explanation

$z=a+\bar{b}c$. $a=1$ gives minterms 4, 5, 6, 7 and $\bar{b}c$ gives 1 and 5. Union: $\sum(1,4,5,6,7)$.