The XOR (^) or exclusive or operator compares two numbers on a bit level and returns a number where the bits of that number are turned on if either of the corresponding bits of the two numbers are 1, but not both.

    a:  00101010   42
    b:  00001111   15       
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a ^ b:  00100101   37

Keep in mind that if a bit is off in both numbers, it stays off in the result. Note that XOR-ing a number with itself will always result in 0.

So remember, for every given bit in a and b:

0 ^ 0 = 0
0 ^ 1 = 1
1 ^ 0 = 1
1 ^ 1 = 0

Therefore:

 111 (7) ^ 1010 (10) = 1101 (13)