GATE 2017 EC (EC2) – Question 26

Digital Circuits · Combinatorial Circuits · 1 mark · Multiple choice

Consider the multiplexer circuit shown. The Boolean expression F implemented by the circuit is

Diagram for GATE 2017 EC (EC2) question 26

$\bar X\bar Y\bar Z+XY+\bar YZ$
$\bar XY\bar Z+XZ+\bar YZ$
$\bar XY\bar Z+XY+YZ$
$\bar X\bar Y\bar Z+XZ+\bar YZ$

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Correct answer: (B) $\bar XY\bar Z+XZ+\bar YZ$

Explanation

The first 2:1 multiplexer has data inputs Y and 0 and select X. Its output is $A=\bar XY$.

The second multiplexer selects A for Z=0 and its complement for Z=1, so $F=A\bar Z+\bar AZ$. By De Morgan, $\bar A=X+\bar Y$.

Substituting gives $F=\bar XY\bar Z+XZ+\bar YZ$, which is **B**.

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