The GATE Grind

GATE 2015 EC – Question 48

Digital Circuits · Combinatorial Circuits · 2 marks · Multiple choice

A 3-input majority gate is defined by the logic function $M(a, b, c) = ab + bc + ca$. Which one of the following gates is represented by the function $M\left(\overline{M(a, b, c)}, M(a, b, \bar{c}), c\right)$?

  1. 3-input NAND gate
  2. 3-input XOR gate
  3. 3-input NOR gate
  4. 3-input XNOR gate

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Show answer and explanation

Correct answer: (B) 3-input XOR gate

Explanation

Let $m = M(a, b, c)$. Then $M(a, b, \bar{c})$ is the majority of $a$, $b$ and $\bar{c}$. Evaluate the function for all eight inputs: it outputs 1 exactly when an odd number of $a$, $b$, $c$ are 1, which is the 3-input exclusive-OR.