What does radix mean?
A radix is a base or root. In mathematics and computing, it is the number used as the foundation of a positional numeral system: binary has radix 2, octal has radix 8, decimal has radix 10, and hexadecimal has radix 16. The place value of every digit depends on that choice, which is why the radix must accompany a numeral when its base is not obvious. In botany, the same word denotes a plant's principal root, from which smaller lateral roots may grow. More generally, “radix” can refer to a fundamental source or basis, though this use is relatively uncommon outside technical writing. The word is especially useful in computing because it names the central organizing principle behind number representation and algorithms such as radix sort. Its Latin ancestry also gives it a broader sense of a root on which a structure depends.
nounA base or root from which other things develop. In mathematics and computing, it denotes the base of a positional numeral system; in botany, it denotes the main root of a plant.
- The base of a positional numeral system, such as 2 for binary or 10 for decimal.
- The principal root of a plant, as distinct from lateral or fibrous roots.
- A fundamental base or origin from which something else develops.
"Binary is the radix of the computer's number system."
"Each digit in a hexadecimal number has a value determined by the radix of 16."
"The seedling's radix grew downward while its shoot rose toward the light."
Both plural forms are established. “Radices” is traditional in mathematics and botany, while “radixes” is common in computing, especially in “radix sorts.”
"The algorithm groups values by digit and then processes the resulting radices in order."
From the Latin word for “root,” radix reveals that every positional number system stands on a chosen foundation: 2, 8, 10, or 16.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does radix come from?
The English word comes from Latin radix, meaning “root” or “base.” It was adopted in mathematics for the base of a numeral system, preserving the metaphor of a number system as something built upon a foundational root. The same Latin source also underlies related words such as radical, radicand, radicle, and eradicate.
How radix is actually used
The term is mainly formal and technical. In computing, it is also commonly encountered in expressions such as “radix sort”; in mathematics, “radix notation” refers to representation according to a chosen base.
Easily confused with radix
A radix is a base or root, whereas a radical is a root symbol in mathematics or a profoundly important or unconventional person or idea.
A radix is a base or root, while a radius is a line segment from the centre of a circle or sphere to its circumference.
A radix is a mathematical or botanical base, whereas a radish is an edible root vegetable.