Definition:Digit

Definition

Let $n$ be a number expressed in a particular number base, $b$ for example.

Then $n$ can be expressed as:

$\sqbrk {r_m r_{m - 1} \ldots r_2 r_1 r_0 . r_{-1} r_{-2} \ldots}_b$

where:

$m$ is such that $b^m \le n < b^{m 1}$;

all the $r_i$ are such that $0 \le r_i < b$.

Each of the $r_i$ are known as the digits of $n$ (base $b$).

It is taken for granted that for base $10$ working, the digits are elements of the set of Arabic numerals: $\set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$.

A digit can also be known as a figure, especially in natural language.

Hence the phrase to figure (something) out, which has the overtone of calculation by arithmetic.

An outdated term for a digit is cipher, also spelt cypher.