Fixed Point Arithmetic

Fixed point arithmetic is a method for representing and performing arithmetic operations on real numbers using integers, where a fixed number of digits are allocated for the fractional part. It is commonly used in embedded systems, digital signal processing, and financial applications where floating-point hardware is unavailable or too costly. This approach provides predictable performance and avoids the rounding errors associated with floating-point arithmetic in certain contexts.

Also known as: Fixed-point math, Fixed-point numbers, Fixed-point representation, Q format, Scaled integers

Why learn Fixed Point Arithmetic?

Developers should learn fixed point arithmetic when working on systems with limited resources, such as microcontrollers or FPGAs, where floating-point units are absent or inefficient. It is essential for applications requiring deterministic behavior, like real-time audio processing, game physics, or financial calculations where exact decimal representation is critical. Using fixed point arithmetic can improve performance and reduce memory usage compared to floating-point alternatives in these scenarios.

Learning Resources

• docs: Fixed Point Arithmetic: An Introduction
• tutorial: Fixed Point Math in C
• course: Fixed Point Arithmetic on Coursera
• video: Fixed Point vs Floating Point - Computerphile
• book: Numerical Recipes: The Art of Scientific Computing