The radix (Latin for root), also called base, is the number of various unique symbols (or digits or numerals) a positional numeral system uses to represent numbers. For example the decimal system uses 10 unique symbols viz. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to represent various numbers and hence has radix 10. The highest symbol of a positional numeral system has the value one less than the value of the radix of that numeral system. For example in the decimal system the highest symbol is nine (9) whose value is one less than the value of the radix of the decimal system, i.e. 10. The various positional numeral systems differ from one another only in the radix they use. (The base itself is almost always expressed in base 10.) A numeral is a symbol or group of symbols that represents a number. ... Decimal, or denary, notation is the most common way of writing the base 10 numeral system, which uses various symbols for ten distinct quantities (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits) together with the decimal point and the sign symbols + (plus) and − (minus) to...

When describing radix in mathematical notation, the letter b is generally used as a symbol for this concept, so, for a binary system, b equals 2. Another common way of expressing the radix is writing it as a subscript (in base ten) after the number that is being represented. 1111011₂ implies that the number 1111011 is a base 2 number, equal to 123₁₀ (a decimal notation representation), 173₈ (octal) and 7B₁₆ (hexadecimal). When using the written abbreviations of number bases, the radix is not printed: Bin 1111011 is the same as 1111011₂. Mathematical notation is used in mathematics, and throughout the physical sciences, engineering, and economics. ... The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ... See also the disambiguation page title equality. ... Decimal, or denary, notation is the most common way of writing the base 10 numeral system, which uses various symbols for ten distinct quantities (0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits) together with the decimal point and the sign symbols + (plus) and − (minus) to... The octal numeral system is the base-8 number system, and uses the digits 0–7. ... In mathematics, hexadecimal or simply hex is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ...

See also

• Mixed radix
• Radix point