structural:reformatting
Notation

When describing base 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 base is writing it as a decimal subscript after the number that is being represented (this notation is used in this article). 1111011 implies that the number 1111011 is a base-2 number, equal to 123 (a decimal notation representation), 173 (octal) and 7B (hexadecimal). In books and articles, when using initially the written abbreviations of number bases, the base is not subsequently printed: it is assumed that binary 1111011 is the same as 1111011.

The base b may also be indicated by the phrase "base- b ". So binary numbers are "base-2"; octal numbers are "base-8"; decimal numbers are "base-10"; and so on.

To a given radix b the set of digits {0, 1,..., b −2, b −1} is called the standard set of digits. Thus, binary numbers have digits {0, 1}; decimal numbers have digits {0, 1, 2,..., 8, 9}; and so on. Therefore, the following are notational errors: 52, 2, 1A. (In all cases, one or more digits is not in the set of allowed digits for the given base.)