What is XOR?

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.