Editing Bitwise operation (section)

===XOR===
[[File:Z2^4; Cayley table; binary.svg|thumb|Bitwise XOR of 4-bit integers]]
A '''bitwise XOR''' is a [[binary operation]] that takes two bit patterns of equal length and performs the [[Exclusive disjunction|logical exclusive OR]] operation on each pair of corresponding bits. The result in each position is 1 if only one of the bits is 1, but will be 0 if both are 0 or both are 1. In this we perform the comparison of two bits, being 1 if the two bits are different, and 0 if they are the same. For example:

     0'''10'''1 (decimal 5)
 XOR 0'''01'''1 (decimal 3)
   = 0'''11'''0 (decimal 6)

The bitwise XOR may be used to invert selected bits in a register (also called toggle or flip). Any bit may be toggled by XORing it with 1. For example, given the bit pattern 0010 (decimal 2) the second and fourth bits may be toggled by a bitwise XOR with a bit pattern containing 1 in the second and fourth positions:

     '''0'''0'''1'''0 (decimal 2)
 XOR '''1'''0'''1'''0 (decimal 10)
   = '''1'''0'''0'''0 (decimal 8)

This technique may be used to manipulate bit patterns representing sets of Boolean states.

[[Assembly language]] programmers and optimizing [[compiler]]s sometimes use XOR as a short-cut to setting the value of a register to zero. Performing XOR on a value against itself always yields zero, and on many architectures this operation requires fewer clock cycles and less memory than loading a zero value and saving it to the register.

If the set of bit strings of fixed length ''n'' (i.e. [[Word (computer architecture)|machine words]]) is thought of as an ''n''-dimensional [[vector space]] <math>{\bf F}_2^n</math> over the [[Field (mathematics)|field]] [[GF(2)|<math>{\bf F}_2</math>]], then vector addition corresponds to the bitwise XOR.