radixlike

Radixlike is a term used to describe numeral systems, representations, or algorithms that resemble a radix-based structure yet do not strictly adhere to a single fixed base for all positional places. In a radixlike representation, numbers are usually expressed in a positional form with digits tied to place values, but the base may vary by position, be non-integer, or permit multiple admissible digits per place.

Common examples include mixed-radix systems, where different positions use different bases (for example, currency and time representations with 60 seconds per minute, 60 minutes per hour, and 24 hours per day); non-integer bases, as in beta-expansions where the base β is a real number greater than 1; and negative-base systems like negabinary, which use a negative base. The factorial number system is another form of radixlike representation, in which weights grow as factorials and the allowable digit range increases with position.

Radixlike systems share the general features of radix-based representations: a set of digits for each position and place-value weights determined by the chosen base pattern. However, because the base is not uniform or is nonstandard, carry rules, normalization procedures, and conversion algorithms must be adapted accordingly.

Radixlike concepts appear in number theory, theoretical computer science, and digital encoding, providing a flexible framework for analyzing nonstandard numeration schemes and their arithmetic properties. See also numeral system, mixed radix, beta-expansion, negabinary, and factoradic.