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Numeral systems by culture
Hindu-Arabic numerals
Eastern Arabic; Indian family; Khmer	Mongolian; Thai; Western Arabic
East Asian numerals
Chinese; Counting rods; Japanese	Korean; Suzhou
Alphabetic numerals
Abjad; Armenian; Āryabhaṭa; Cyrillic	Ge'ez; Greek (Ionian); Hebrew
Other systems
Attic; Babylonian; Brahmi; Egyptian; Etruscan; Inuit	Mayan; Quipu; Roman; Urnfield
	List of numeral system topics
Positional systems by base
	Decimal (10)
	1, 2, 3, 4, 5, 8, 12, 16, 20, 60, more…
	v • d • e

For other uses, see Radix (disambiguation).

In arithmetic, the radix or base refers to the number b in an expression of the form bⁿ. The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power" or "b to the power n". The term power strictly refers to the entire expression, but is sometimes used to refer to the exponent.

When b is an integer bigger than 1, this process is particularly important in positional numeral systems for denoting numbers. For a given integer b the positional numeral system is called base b.

In general, b and n can be arbitrary real or complex numbers.

The inverse function to exponentiation with base b (when it is well-defined) is called the logarithm with base b, denoted log_b. Thus:

$\log_b (b^n) = b^{\log_b (n)} = n.$

[edit] Etymology

Radix is a Latin word meaning root (e.g. "eradicate", to pull up from the root; destroy); root can be considered a synonym for base in the arithmetical sense.

[edit] Bases and positional numeral systems

Also see the table to the right.

In mathematical numeral systems, the base or radix is usually the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system (the most common system in use today) the radix is 10, because it uses the 10 digits from 0 through 9.

Examples of numeral systems:

The decimal system, the most used system of numbers in the world, is used in arithmetic. Its ten digits are "0-9".
The binary numeral system, widely used in computing, is base two. The two digits are "0" and "1".
The octal system, which is base 8, is also often used in computing. The eight digits are "0-7".
Also in widespread use in computing is the hexadecimal system. It is base 16, and the 16 digits are "0-9" followed by "A-F".

[edit] External links