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GATE 2019 CS – Question 40

Digital Logic · Combinational Circuits · 2 marks · Multiple choice

Consider three 4-variable functions $f_1$, $f_2$, and $f_3$, which are expressed in sum-of-minterms as

$f_1=\Sigma(0,2,5,8,14)$, $f_2=\Sigma(2,3,6,8,14,15)$, $f_3=\Sigma(2,7,11,14)$.

For the following circuit with one AND gate and one XOR gate, the output function $f$ can be expressed as:

Diagram for GATE 2019 CS question 40
  1. $\Sigma(7,8,11)$
  2. $\Sigma(2,7,8,11,14)$
  3. $\Sigma(2,14)$
  4. $\Sigma(0,2,3,5,6,7,8,11,14,15)$

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Show answer and explanation

Correct answer: (A) $\Sigma(7,8,11)$

Explanation

The output is $f=(f_1\cdot f_2)\oplus f_3$. $f_1f_2=\Sigma(2,8,14)$, and XORing with $f_3=\Sigma(2,7,11,14)$ cancels the common minterms 2 and 14, leaving $\Sigma(7,8,11)$.