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  • 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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