Explain using xor to find two non-duplicate integers in an array

Question

Given [1,1,4,5,5,6] we can find 4 and 6 to be the non-repeating integers.

There is a solution using XOR.

Answer 1

When you xor two equal values, they cancel out. This allows to reveal the non-repeating pair.

XOR(aabbccddeeffgh) = XOR(gh) = ...1...

Knowing any bit on which g and h differ allows to set g and h aside in two subsets:

...0... => XOR(aabbcceeg) = g

...1... => XOR(ddffh) = h