Editing Fixed-point arithmetic (section)

===Scaling and renormalization===
Typical processors do not have specific support for fixed-point arithmetic. However, most computers with binary arithmetic have fast [[bit shift]] instructions that can multiply or divide an integer by any power of 2; in particular, an [[arithmetic shift]] instruction.  These instructions can be used to quickly change scaling factors that are powers of 2, while preserving the sign of the number.

Early computers like the [[IBM 1620]] and the [[Burroughs Medium Systems|Burroughs B3500]] used a [[binary-coded decimal]] (BCD) representation for integers, namely base 10 where each decimal digit was independently encoded with 4 bits. Some processors, such as microcontrollers, may still use it.  In such machines, conversion of decimal scaling factors can be performed by bit shifts and/or by memory address manipulation.

Some DSP architectures offer native support for specific fixed-point formats, for example, signed ''n''-bit numbers with ''n''−1 fraction bits (whose values may range between −1 and almost +1). The support may include a multiply instruction that includes renormalization—the scaling conversion of the product from 2''n''−2 to ''n''−1 fraction bits.{{cn|date=July 2021}} If the CPU does not provide that feature, the programmer must save the product in a large enough register or temporary variable, and code the renormalization explicitly.