Editing Positional notation (section)

=== Notation ===
When describing base in [[mathematical notation]], the letter ''b'' is generally used as a [[symbol]] for this concept, so, for a [[Binary numeral system|binary]] system, ''b'' [[equality (mathematics)|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<sub>2</sub> implies that the number 1111011 is a base-2 number, equal to 123<sub>10</sub> (a [[decimal notation]] representation), 173<sub>8</sub> ([[octal]]) and 7B<sub>16</sub> ([[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<sub>2</sub>.

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 {{nowrap|{0, 1, 2, ..., 8, 9};}} and so on. Therefore, the following are notational errors: 52<sub>2</sub>, 2<sub>2</sub>, 1A<sub>9</sub>. (In all cases, one or more digits is not in the set of allowed digits for the given base.)