bitwise XOR

Bitwise XOR or bitwise exclusive OR is a bit-level operationMathworldPlanetmath on two binary values which indicates which bits are set in only one value. For each position i, if the bit di in one value is 1 and the other is 0, then di of the result is 1, otherwise it’s 0. If both input di are 1, the output di is 0. then For example, given 50 and 163 in two unsigned bytes, a bitwise XOR returns 145.

0 0 1 1 0 0 1 0
XOR 1 0 1 0 0 0 1 1
= 1 0 0 1 0 0 0 1

Given a Mersenne number of the form 2k-1 (where k is the bit size of the data type in use, e.g., 8 for bytes, 16 for words, 32 for double words, etc.) and some smaller integer n, XORing that Mersenne number with n has the same effect as performing a bitwise NOT on n. Or, given m and n, XORing them has the same effect as m-n (subject to some caveats about the sign bit, or if the values are unsigned, the effect is then the same as |m-n|). XORing two values that are the same gives 0.

Title bitwise XOR
Canonical name BitwiseXOR
Date of creation 2013-03-22 17:02:52
Last modified on 2013-03-22 17:02:52
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 4
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A63
Related topic BitwiseAND
Related topic BitwiseOR
Related topic BitwiseNOT