Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

Description

It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true; the exclusive or operator 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 and B".

More generally, XOR is true only when an odd number of inputs are 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.

The negation of XOR is logical biconditional, which outputs true only when both inputs are the same.

See also

• Affirming a disjunct
• Ampheck
• Boolean algebra
• Boolean domain
• Boolean function
• Boolean-valued function
• Controlled NOT gate
• Disjunctive syllogism
• First-order logic
• Inclusive or
• Involution (mathematics)
• List of Boolean algebra topics
• Logical biconditional
• Logical connective
• Logical graph
• Logical value - see Truth value
• Material conditional
• Operation (mathematics)
• Paradox of material implication
• Parity bit
• Propositional calculus
• Rule 90
• Symmetric difference
• Truth value
• XOR cipher
• XOR gate
• XOR linked list

External links

• Exclusive or @ Wikipedia