Definition

1. Noun:
   • Base of a numeral system: In mathematics and computing, "radix" refers to the number of unique digits, including zero, used to represent numbers in a positional numeral system. It is the base number that determines the value of each digit's place.
   • Root or source: In more formal or technical contexts, "radix" can mean the root, origin, or foundation of something, though this usage is less common.

Examples of Usage

• Noun:
  • In the binary system, the radix is 2.
  • The radix of the hexadecimal system is 16.
  • The concept of zero is crucial for positional systems with any radix.

Advanced Usage

• "Mixed radix": A numeral system where different digit positions have different bases.
  • Representing time (hours, minutes, seconds) uses a mixed radix system.
• "Radix point": The generalization of a decimal point; it separates the integer part from the fractional part in any base.
  • In binary, the radix point is sometimes called the "binary point."

Variants and Related Words

• Radices (n): The plural form of "radix."
  • Different ancient cultures used various radices for their counting systems.
• Radical (adj): Pertaining to the root or origin; fundamental. (Shares the same Latin root , meaning "root.")
  • A radical change is one that goes to the root of the matter.

Synonyms

• Base: The most common synonym in mathematics.
  • The base-10 system is familiar to most people.
• Root: A synonym in the context of origin or source.

Related Phrases and Technical Terms

• Radix sort: A non-comparative integer sorting algorithm that groups numbers by their individual digits.
  • Radix sort is efficient for sorting lists of integers.
• Radix complement: In numeral systems, a method for representing negative numbers (e.g., two's complement in binary).
  • The radix complement is essential for computer arithmetic.

Related Idioms

(Note: As a highly technical term, "radix" is not commonly used in idiomatic expressions. Its usage is primarily confined to mathematical and computing contexts.)

Noun

1. (numeration system) the positive integer that is equivalent to one in the next higher counting place
   • 10 is the radix of the decimal system