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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 gate. [1] It is equivalent to the logical connective ( ↔ {\displaystyle \leftrightarrow } ) from mathematical logic , also known as the material biconditional.
definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
This explains why "EQ" is often called "XNOR" in the combinational logic of circuit engineers, since it is the negation of the XOR operation; "NXOR" is a less commonly used alternative. [1] Another rationalization of the admittedly circuitous name "XNOR" is that one begins with the "both false" operator NOR and then adds the eXception "or both ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
The material equivalence of and (often written as ) is itself another statement in the same object language as and . This statement expresses the idea "' p {\displaystyle p} if and only if q {\displaystyle q} '".
The gate is called XNOR because it is a NOR gate with an added twist. With NOR, if either or both inputs is 1, the output is 0. With XNOR, the "exclusive" condition is added to that, so that with XNOR, the output is 0 only if exactly one input is 1. With XNOR, the "both inputs 1" condition is excluded from producing the active output, namely 0.
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs.