Exclusive Or Operation
(Redirected from XOR)
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An Exclusive Or Operation is a boolean logic operation that ...
- AKA: XOR.
- Context:
- It cannot be modeled by a Linear Mapping.
- …
- Counter-Example(s):
- See: Logical Connective, Table of Logic Symbols, Infix, Logical Biconditional, Operand, Venn Diagram, Boolean Logic System, Set Symmetric Difference Operation.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/exclusive_or Retrieved:2015-1-31.
- Exclusive disjunction or exclusive or is a logical operation that outputs true whenever both inputs differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR, EOR, EXOR, ⊻, ⊕, ↮, and ≢. The opposite of XOR is logical biconditional, which outputs true whenever both inputs are the same.
It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true; exclusive or excludes that case. This is sometimes thought of as "one or the other but not both". This could be written as A or B but not A & B.
More generally, XOR is true whenever an odd number of inputs is true. A chain of XORs — a XOR b XOR c XOR d (and so on) — is true whenever an odd number of the inputs are true and is false whenever an even number of inputs are true.
- Exclusive disjunction or exclusive or is a logical operation that outputs true whenever both inputs differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR, EOR, EXOR, ⊻, ⊕, ↮, and ≢. The opposite of XOR is logical biconditional, which outputs true whenever both inputs are the same.