Gates: XOR properties

More XOR tricks (amaze your friends!):

Classic swap problem (early CMSC 106)

temp = x;

x = y;

y = temp;

Using XOR:

x = x ^ y ;

y = x ^ y ;

x = x ^ y ;

Let x0 be the original value of x, y0 be the original value of y:

x = x ^ y = x0 ^ y0

y = x ^ y = (x0 ^ y0) ^ y0

Substitute for x

= x0 ^ (y0 ^ y0)

Associative property

= x0 ^ 0

x ^ x = 0

= x0

Identity

x = x ^ y = (x0 ^ y0) ^ x0

Substitute for x and y

= (x0 ^ x0) ^ y0

Associative, symmetric properties

= 0 ^ y0

x ^ x = 0

= y0

Identity

What other operator is a less-safe way of doing this?