User:Dimawik/Computer arithmetic

Computer arithmetic is a subfield of the computer architecture that deals with both the hardware implementation of arithmetic operations in a computer and software algorithms supporting the arithmetic, with an emphasis on speeding up the numeric calculations. The term also designates the corresponding branch of the computer engineering.

The field of computer arithmetic covers hardware implementation of adders (including counters) and subtractors, multipliers, dividers, square rooters and evaluators for other arithmetic functions. The software side of the computer arithmetic involves design and analysis of arithmetic algorithms. Bitwise operations like NOT, AND, OR, XOR, bit shifts also belong to "computer arithmetic".

Integer numbers
While multiple number representations were historically considered and used (including binary coded decimal tribit, and residue number system), modern computer almost exclusively use the binary representation. For the signed integers the two's complement approach is typical (for example, 4-bit integers have a range from -8 (1000) to +7 (0111).

Real numbers
The real numbers are treated as a combination of a whole (a.k.a. integral part) and a fractional part) expressed as a single sequence of bits. The position of a radix point separating the parts is implied (fixed). For example, a signed "1+3" integer uses 4 bits, three of which represent the fractional part (with the accuracy of $1/8$ and range from -1 coded as binary 1.000 to +0.875 coded as 0.111).