Home › Previous year questions › GATE 2016 CS (CS2) › Question 18GATE 2016 CS (CS2) – Question 18 Digital Logic · Boolean Algebra and Minimization · 1 mark · Multiple choice
Boolean variables satisfy $x_1\oplus x_2\oplus x_3\oplus x_4=0$. Which must hold?
$x_1x_2x_3x_4=0$ $x_1x_3+x_2=0$ $\bar x_1\oplus\bar x_3=\bar x_2\oplus\bar x_4$ $x_1+x_2+x_3+x_4=0$ Practise this question in The GATE Grind →
Show answer and explanation Correct answer: (C) $\bar x_1\oplus\bar x_3=\bar x_2\oplus\bar x_4$
Explanation Rearrange to $x_1\oplus x_3=x_2\oplus x_4$. Since complementing both XOR inputs preserves its value, $\bar a\oplus\bar b=a\oplus b$. Thus C always follows; the remaining expressions fail on even-parity counterexamples.
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