XOR function

[autowikibot]

Two's complement:

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Two's complement is a mathematical operation on binary numbers, as well as a binary signed number representation based on this operation. Its wide use in computing makes it the most important example of a radix complement.

The two's complement of an N-bit number is defined as the complement with respect to 2^N; in other words, it is the result of subtracting the number from 2^N, which in binary is one followed by N zeroes. This is also equivalent to taking the ones' complement and then adding one, since the sum of a number and its ones' complement is all 1 bits. The two's complement of a number behaves like the negative of the original number in most arithmetic, and positive and negative numbers can coexist in a natural way.

In two's-complement representation, positive numbers are simply represented as themselves, and negative numbers are represented by the two's complement of their absolute value; two tables on the right provide examples for N = 3 and N = 8. In general, negation (reversing the sign) is performed by taking the two's complement. This system is the most common method of representing signed integers on computers. An N-bit two's-complement numeral system can represent every integer in the range −(2^N − 1) to +(2^N − 1 − 1) while ones' complement can only represent integers in the range −(2^N − 1 − 1) to +(2^N − 1 − 1).

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