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The XNOR gate is a digital logic gate whose function is the logical complement of the Exclusive OR gate. It is equivalent to the logical connective 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 results if both of the inputs to the gate are the same. If one but not both inputs are high , a low output results.
The algebraic notation used to represent the XNOR operation is S = A ⊙ B {\displaystyle S=A\odot B}. The algebraic expressions ⋅ {\displaystyle \cdot } and A ⋅ B + A ¯ ⋅ B ¯ {\displaystyle A\cdot B+{\overline {A}}\cdot {\overline {B}}} both represent the XNOR gate with inputs A and B.