Fixed-point arithmetic

Fixed-point arithmetic represents numbers as integers with an implied radix point at a fixed position. It offers predictable precision and range, often with simpler hardware than floating-point arithmetic.

Scaling (numerical analysis): Multiplying a quantity by a known factor to change its numerical magnitude or units. A scale factor places the implied point and determines the value represented by an integer.
Floating-point arithmetic: A numerical representation that stores a significand and exponent, allowing the radix point to move across a wide range. Its variable exponent trades fixed-point's uniform spacing for much greater dynamic range.
Digital signal processing: The analysis and transformation of signals represented as discrete numerical samples. Fixed-point arithmetic is common in processors designed for efficient real-time signal operations.
Binary number: A number represented using the base-two positional numeral system. Binary fixed-point formats locate an implied point among powers of two.
Numerical stability: The sensitivity of a numerical computation's output to small changes in its inputs or intermediate errors. Quantization and overflow can amplify errors through repeated fixed-point operations.
Quantization (signal processing): Mapping a continuous or finely spaced set of values onto a finite set of discrete levels. Fixed-point formats approximate values between their representable levels through quantization.
Integer arithmetic: Arithmetic on whole-number values represented without fractional parts. Fixed-point uses integer operations internally but assigns those integers fractional meaning through scaling.
Digital signal processor: A microprocessor optimized for operations used in digital signal processing. Many DSPs provide fixed-point instructions for fast, low-power filtering and transforms.
Positional notation: A numeral system in which a digit's value depends on its position and the system's base. The implied point separates integer and fractional place values in a positional representation.
Saturation arithmetic: Arithmetic in which results beyond the representable range are clamped to the nearest limit. Saturation is a common alternative to wraparound when fixed-point values overflow.

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