fixedbase

FixedBase is a term used in mathematics and computer science to denote systems that use a fixed numerical base for representing and manipulating numbers. In a FixedBase representation, each digit position corresponds to a fixed power of a base b, so the value of a number is computed as the sum of digit_i times b^i. This is the standard model of positional numeral systems, with common bases such as binary (base 2), decimal (base 10), and hexadecimal (base 16). The term is often used in contrast with nonstandard or mixed-radix representations where the base changes from position.

FixedBase can also describe encoding schemes that map integers to strings using a fixed alphabet of size b, enabling straightforward lexicographic ordering and conversion to/from numeric values.

In computer arithmetic, fixed-base systems enable efficient hardware and software implementations. Arithmetic operations—addition, subtraction, multiplication, division—are performed using fixed-base algorithms; base conversion between FixedBase representations is a well-studied problem; conversion cost depends on the base and word size.

Applications of FixedBase concepts include computer arithmetic, data encoding, error-checking schemes, and educational tools for teaching place-value concepts. The framework is used to analyze performance characteristics of arithmetic pipelines, memory layouts, and encoding schemes that rely on a stable, uniform base across all digit positions.

Because FixedBase is not a single standardized specification, the term is used descriptively in various sources to denote any system that adheres to a fixed base across digits. See also: positional numeral system, radix, base conversion, fixed-point arithmetic.