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.)

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.

See also

• Mixed radix
• Radix point