XNOR gate

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Logical connectives
NOT ${\displaystyle \neg A,-A,{\overline {A}},\sim A}$ AND ${\displaystyle A\land B,A\cdot B,AB,A\ \&\ B,A\ \&\&\ B}$ NAND ${\displaystyle A{\overline {\land }}B,A\uparrow B,A\mid B,{\overline {A\cdot B}}}$ OR ${\displaystyle A\lor B,A+B,A\mid B,A\parallel B}$ NOR ${\displaystyle A{\overline {\lor }}B,A\downarrow B,{\overline {A+B}}}$ XNOR ${\displaystyle A\odot B,{\overline {A{\overline {\lor }}B}}}$ └ equivalent ${\displaystyle A\equiv B,A\Leftrightarrow B,A\leftrightharpoons B}$ XOR ${\displaystyle A{\underline {\lor }}B,A\oplus B}$ └nonequivalent ${\displaystyle A\not \equiv B,A\not \Leftrightarrow B,A\nleftrightarrow B}$ implies ${\displaystyle A\Rightarrow B,A\supset B,A\rightarrow B}$ nonimplication (NIMPLY) ${\displaystyle A\not \Rightarrow B,A\not \supset B,A\nrightarrow B}$ converse ${\displaystyle A\Leftarrow B,A\subset B,A\leftarrow B}$ converse nonimplication ${\displaystyle A\not \Leftarrow B,A\not \subset B,A\nleftarrow B}$
Related concepts
Propositional calculus Predicate logic Boolean algebra Truth table Truth function Boolean function Functional completeness Scope (logic)
Applications
Digital logic Programming languages Mathematical logic Philosophy of logic
Category
v t e

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 (${\displaystyle \leftrightarrow }$) 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 ${\displaystyle S=A\odot B}$. The algebraic expressions ${\displaystyle (A+{\overline {B}})\cdot ({\overline {A}}+B)}$ and ${\displaystyle A\cdot B+{\overline {A}}\cdot {\overline {B}}}$ both represent the XNOR gate with inputs A and B.