radices

Radix is the Latin word for root or base, and radices is its plural. In mathematics and related disciplines, radix most often refers to the base of a numeral system. In a positional numeral system with base b, digits range from 0 to b−1, and the value of a multi-digit numeral is computed as a sum of digits times powers of b. The decimal system has radix 10, binary has radix 2, and hexadecimal has radix 16. The choice of radix affects digit symbols and arithmetic algorithms; logarithms with base b measure orders of magnitude.

Outside pure numeracy, radix has other specialized senses. In anatomy and botany, radix denotes the base or origin of a structure: for example, the root of a tooth is called radix dentis; a vessel or nerve may have a radix at its origin. In linguistics, the term radix (or radices) can mean the root form of a word from which affixes are derived; it is related to the concept of a root in morphology. In historical linguistics, radices may be identified as etymons in philology.

In computer science, radix appears in sorting and numeric representation. Radix sort is a non-comparative sorting algorithm that processes digits from least significant to most significant in a fixed base. In floating-point formats, the radix underlies the representation of the significand and exponent in some schemes.