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XNOR Gate ○꠹｜Definition｜1st｜20251119205401-00-⌔

XNOR gate - Wikipedia

XNOR gate

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The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate.¹ It is equivalent to the logical connective ($\leftrightarrow$) from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an “equivalence gate”. A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results.

The algebraic notation used to represent the XNOR operation is $S=A\odot B$. The algebraic expressions $(A+\overline{B})\cdot (\overline{A}+B)$ and $A\cdot B+\overline{A}\cdot \overline{B}$ both represent the XNOR gate with inputs A and B.

Printed 2026-06-28.

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Footnotes

1. “Exclusive-NOR Gate Tutorial”. 22 August 2013. Retrieved 6 May 2018. ↩

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