# Definition:Digit

(Redirected from Definition:Cipher (Digit))

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## 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: $\set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$.

## Also known as

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An outdated term for a **digit** is **cipher**, also spelt **cypher**.

## Also see

- Results about
**digits**can be found**here**.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): Glossary - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**digit** - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): Glossary - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**digit**