Fixed-point arithmetic is a numerical representation and computation method where numbers are represented with a fixed number of digits before and after the decimal point (or binary point). Unlike floating-point arithmetic, which can represent a wide range of values by using a variable number of significant digits and exponents, fixed-point arithmetic has a predetermined level of precision and range. ### Key Characteristics of Fixed-point Arithmetic: 1. **Representation**: The numbers are represented as integers multiplied by a scaling factor.
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Fixed-point arithmetic represents values as integer multiples of a fixed scale . Integer operations on , followed by the required rescaling and rounding, implement arithmetic on these values. Unlike floating-point arithmetic, the spacing is constant throughout the representable range.
For , the stored integer represents . Multiplying two encoded values and gives , so returning to the original scale requires dividing the integer product by with a stated rounding rule. Fixed spacing makes resolution predictable, but the chosen integer width limits range and can cause integer overflow.