Definition

Noun: A fixed-point number is a method of representing a real number within a computer or digital system where the position of the decimal (or binary) point is fixed and predetermined. This contrasts with floating-point representation, where the point's position can vary.

Usage

A fixed-point number is specified by its total number of digits and the fixed position of the radix point (e.g., decimal point or binary point). It is commonly used in systems where processing speed is critical and the range of values is known and limited, such as in embedded systems, digital signal processing, or financial calculations that require exact decimal representation.

Examples

• The microcontroller uses fixed-point numbers for its calculations to ensure deterministic timing.
• Storing currency values as fixed-point numbers with two decimal places prevents rounding errors common in floating-point arithmetic.
• In this format, the number 123.45 is represented as an integer 12345, with the understanding that the point is fixed two digits from the right.

Advanced Usage

• Fixed-point arithmetic: Refers to mathematical operations (addition, subtraction, multiplication, division) performed on fixed-point numbers. These operations often require specific scaling and shifting to manage the position of the implied radix point.
• Q-format notation: A common convention for describing fixed-point numbers, e.g., Q15 format indicates 1 sign bit and 15 fractional bits.

Variants and Related Words

• Fixed-point notation (n): The system or format for representing numbers with a fixed radix point.
• Fixed-point representation (n): Synonymous with fixed-point notation.

Synonyms

• Scaled integer
• (In contrast) Antonym: Floating-point number

Related Phrases

• To use fixed-point: To employ a fixed-point number representation.
  • The algorithm was designed to use fixed-point for greater efficiency.
• Fixed-point precision: The level of detail or number of fractional digits available in a fixed-point format.
  • Increasing the fixed-point precision from Q10 to Q15 improved the output quality.

Noun

1. a number represented in fixed-point notation