It's my understanding that when you XOR something, the result is the sum of the two numbers mod $2$.
Why then does $4 \oplus 2 = 6$ and not $0$? $4+2=6$, $6%2$ doesn't equal $6$. I must be missing something about what "addition modulo 2" means, but what?
100 // 4
010 // XOR against 2
110 = 6 // why not zero if xor = sum mod 2?