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2. Two's complement - Wikipedia

   en.wikipedia.org/wiki/Two's_complement

   Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...

3. Signed number representations - Wikipedia

   en.wikipedia.org/wiki/Signed_number_representations

   Addition of a pair of two's-complement integers is the same as addition of a pair of unsigned numbers (except for detection of overflow, if that is done); the same is true for subtraction and even for N lowest significant bits of a product (value of multiplication). For instance, a two's-complement addition of 127 and −128 gives the same ...

4. Method of complements - Wikipedia

   en.wikipedia.org/wiki/Method_of_complements

   Subtraction is done by adding the ten's complement of the subtrahend, which is the nines' complement plus 1. The result of this addition is used when it is clear that the difference will be positive, otherwise the ten's complement of the addition's result is used with it marked as negative.

5. Bit numbering - Wikipedia

   en.wikipedia.org/wiki/Bit_numbering

   This table illustrates an example of an 8 bit signed decimal value using the two's complement method. The MSb most significant bit has a negative weight in signed integers, in this case -2 7 = -128. The other bits have positive weights. The lsb (least significant bit) has weight 2 0 =1. The signed value is in this case -128+2 = -126.

6. Adder–subtractor - Wikipedia

   en.wikipedia.org/wiki/Adder–subtractor

   Input 1 (I 1) is A; that has control input D that is also connected to the initial carry, then the modified adder performs addition when D = 0, or; subtraction when D = 1. This works because when D = 1 the A input to the adder is really A and the carry in is 1. Adding B to A and 1 yields the desired subtraction of B − A.

7. Sign extension - Wikipedia

   en.wikipedia.org/wiki/Sign_extension

   If the source of the operation is an unsigned number, then zero extension is usually the correct way to move it to a larger field while preserving its numeric value, while sign extension is correct for signed numbers. In the x86 and x64 instruction sets, the movzx instruction ("move with zero extension") performs this function.