Editing Two's complement (section)

==Converting from two's complement representation==
A two's-complement number system encodes positive and negative numbers in a binary number representation. The weight of each bit is a power of two, except for the [[most significant bit]], whose weight is the negative of the corresponding power of two.

The value&nbsp;{{mvar|w}} of an {{mvar|N}}-bit integer <math>a_{N-1} a_{N-2} \dots a_0</math> is given by the following formula:

<math display="block">w = -a_{N-1} 2^{N-1} + \sum_{i=0}^{N-2} a_i 2^i</math>

The most significant bit determines the sign of the number and is sometimes called the [[sign bit]]. Unlike in [[sign-and-magnitude]] representation, the sign bit also has the weight {{math|−(2<sup>''N'' − 1</sup>)}} shown above. Using {{mvar|N}} bits, all integers from {{math|−(2<sup>''N'' − 1</sup>)}} to {{math|2<sup>''N'' − 1</sup> − 1}} can be represented.