bitwise XOR

Bitwise XOR or bitwise exclusive OR is a bit-level operation on two binary values which indicates which bits are set in only one value. For each position $i$, if the bit $d_i$ in one value is 1 and the other is 0, then $d_i$ of the result is 1, otherwise it’s 0. If both input $d_i$ are 1, the output $d_i$ 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 $2^k-1$ (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