GATE 2025 EC – Question 23
A 3-input majority logic gate has inputs $X$, $Y$, and $Z$. The output $F$ of the gate is logic ‘1’ if two or more of the inputs are logic ‘1’. The output $F$ is logic ‘0’ if two or more of the inputs are logic ‘0’.
Which one of the following options is a Boolean expression of the output $F$?
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Correct answer: (A) $XY+YZ+ZX$
Explanation
$F=1$ exactly when at least two inputs are 1, i.e. when $XY=1$, $YZ=1$ or $ZX=1$. So $F=XY+YZ+ZX$. The XOR is 1 for an odd number of ones (it is 1 for $XYZ=100$), and the OR and AND forms fail the two-out-of-three rule.