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Exclusive nor (usual symbol '''XNOR''' occasionally '''XAND''' ) is a Logical Operator in Boolean Algebra . It gives the result " True " if both inputs are identical, and " False " if they are different, i.e. it is Equality for Boolean Value s, also called Logical Biconditional , or If And Only If .


DEFINITION

"A XNOR B" is equivalent to: "(A AND B) OR (!A AND !B)".


A \underline{\oplus} B = \lnot(A \oplus B) = (A \land B) \lor (\lnot A \land \lnot B)


For two inputs ''A'' and ''B'', the Truth Table of the operator is as follows.


SYMBOL

The mathematical symbol for exclusive nor varies in the literature. In addition to the abbreviation "xnor", one may see
  • a wedge that is modified in some way, such as being underlined ("∧", or ''⩟''); this is used because exclusive nor is a modification of ordinary (inclusive) Conjunction , which is typically denoted by a wedge ("∧").

    • Similarly, different textual notations are used, including "XAND" (eXclusive AND), " Iff " (if-and-only-if), and "EQV".



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