Positional notation
Digits and numerals

A digit is a symbol that is used for positional notation, and a numeral consists of one or more digits used for representing a number with positional notation. Today's most common digits are the decimal digits "0", "1", "2", "3", "4", "5", "6", "7", "8", and "9". The distinction between a digit and a numeral is most pronounced in the context of a number base.

A non-zero numeral with more than one digit position will mean a different number in a different number base, but in general, the digits will mean the same. For example, the base-8 numeral 23 contains two digits, "2" and "3", and with a base number (subscripted) "8". When converted to base-10, the 23 is equivalent to 19, i.e. 23 = 19. In our notation here, the subscript " " of the numeral 23 is part of the numeral, but this may not always be the case.

Imagine the numeral "23" as having an ambiguous base number. Then "23" could likely be any base, from base-4 up. In base-4, the "23" means 11, i.e. 23 = 11. In base-60, the "23" means the number 123, i.e. 23 = 123. The numeral "23" then, in this case, corresponds to the set of base-10 numbers {11, 13, 15, 17, 19, 21, 23,..., 121, 123} while its digits "2" and "3" always retain their original meaning: the "2" means "two of", and the "3" means "three of".

In certain applications when a numeral with a fixed number of positions needs to represent a greater number, a higher number-base with more digits per position can be used. A three-digit, decimal numeral can represent only up to 999. But if the number-base is increased to 11, say, by adding the digit "A", then the same three positions, maximized to "AAA", can represent a number as great as 1330. We could increase the number base again and assign "B" to 11, and so on (but there is also a possible encryption between number and digit in the number-digit-numeral hierarchy). A three-digit numeral "ZZZ" in base-60 could mean 215 999. If we use the entire collection of our alphanumerics we could ultimately serve a base- 62 numeral system, but we remove two digits, uppercase "I" and uppercase "O", to reduce confusion with digits "1" and "0". We are left with a base-60, or sexagesimal numeral system utilizing 60 of the 62 standard alphanumerics. (But see Sexagesimal system below.) In general, the number of possible values that can be represented by a d {\displaystyle d} digit number in base r {\displaystyle r} is r d {\displaystyle r^{d}}.

The common numeral systems in computer science are binary (radix 2), octal (radix 8), and hexadecimal (radix 16). In binary only digits "0" and "1" are in the numerals. In the octal numerals, are the eight digits 0–7. Hex is 0–9 A–F, where the ten numerics retain their usual meaning, and the alphabetics correspond to values 10–15, for a total of sixteen digits. The numeral "10" is binary numeral "2", octal numeral "8", or hexadecimal numeral "16".
length_constraints:number_words[412]