exclusive or


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exclusive or

[ik¦sklü·siv ′ȯr]
(computer science)
An instruction which performs the “exclusive or” operation on a bit-by-bit basis for its two operand words, usually storing the result in one of the operand locations. Abbreviated XOR.
(mathematics)
A logic operator which has the property that if P is a statement and Q is a statement, then P exclusive or Q is true if either but not both statements are true, false if both are true or both are false.

exclusive or

(logic)
(XOR, EOR) /X or, E or/ A two-input Boolean logic function whose result is true if one input is true and the other is false. The truth table is

A | B | A xor B --+---+-------- F | F | F F | T | T T | F | T T | T | F

The output is thus true if the inputs are not equal. If one input is false, the other is passed unchanged whereas if one input is true, the other is inverted.

In Boolean algebra, exclusive or is often written as a plus in a circle: "⊕". The circle may be omitted suggesting addition modulo two.

In digital logic, an exclusive or logic gate is drawn like a normal inclusive or gate but with a curved line across both inputs: exclusive or gate.

XOR

(eXclusive OR) A Boolean logic operation that is widely used in cryptography as well as in generating parity bits for error checking and fault tolerance. XOR compares two input bits and generates one output bit. The logic is simple. If the bits are the same, the result is 0. If the bits are different, the result is 1.

Several Symbols
Various symbols are used to designate the XOR operation including a + sign inside a circle, an underlined "V" and the caret (^). See cryptography, RAID and or.


XOR in Cryptography
This example uses XOR and the same "secret key" to encrypt and decrypt. Although XOR logic may be used, secret key algorithms are much more sophisticated than this. See encryption algorithm.