XOR (Exclusive-OR)
XOR is known as ‘Exclusive-OR’ and it is a Boolean operator that returns a TRUE when only one of the operands is TRUE and returns a FALSE when both of the operands are either TRUE or FALSE. It is a logical operation on two logical values. Going by the rules of material implication and material equivalence, the exclusive-or is equivalent to the negation of the logical bi-conditional.
Properties
- XOR is an associative operation i.e. re-arranging the parenthesis in an expression having two or more same associative operators in a row does not change the end result. The end result is not affected by the order in which the operations are performed.
( p + q ) + r = p + ( q + r ) - XOR is a commutative operation i.e. the end result is not affected by the order of the terms.
p + q = q + p - It is a linear binary function.
Usage
- Exclusive-OR is used in bitwise operations to check whether the two bits are equal or not.
In logical circuits, a XOR gate can be used to generate a simple adder to add the numbers. - In computer graphics, XOR based drawing methods are generally used to manage items like cursors.
- It is used in signed binary arithmetic operations to detect the overflow.
- It is also used for creating parity information in RAID 3-6.
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