GATE 2014 EC (EC1) – Question 50

Digital Circuits · Combinatorial Circuits · 2 marks · Multiple choice

Find output F of the digital logic circuit shown.

Diagram for GATE 2014 EC (EC1) question 50

$\overline XYZ+X\overline Y\overline Z$
$\overline XY\overline Z+X\overline Y\overline Z$
$\overline X\overline YZ+XYZ$
$\overline X\overline Y\overline Z+XYZ$

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Correct answer: (A) $\overline XYZ+X\overline Y\overline Z$

Explanation

The AND inputs are X XOR Y and Y XNOR Z. Both are1 exactly when X differs from Y and Y equals Z. The two allowed input triples are(0,1,1) and(1,0,0), giving **F=X̄YZ+XȲZ̄,A**. The crossing without a connection dot does not short the two logic outputs.