XOR.md

XOR (Exclusive OR)

Self-inverse property

x ^ x = 0
x ^ 0 = x
x ^ (~x) = -1

Commutativity

x ^ y = y ^ x

Associativity

(a ^ b) ^ c = a ^ (b ^ c)

Distributive Property

(A ^ B) & C = (A & C) ^ (B & C)
A ^ (B + C) = (A ^ B) + (A ^ C)
...

XOR Equation

Equation like a = b ^ x or a = x ^ b can be solved like: x = a ^ b

Alternative XOR Implementations

x ^ y = (x & y) | (x & y)
x ^ y = (x | y) & (x | y)
x ^ y = (x | y) & (x & y)
x ^ y = (x | y) - (x & y);
x ^ y = (x | y) & (~x | ~y);
x ^ y = (x & (~x)) | ((~x) & x);
x ^ y = (x + y - (2 * (x & y)));