# Definition:Basis Representation

## Definition

Let $b \in \Z$ be an integer such that $b > 1$.

Let $n \in \Z$ be an integer such that $n \ne 0$.

The representation of $n$ to the base $b$ is the unique string of digits:

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

where $\pm$ is:

the negative sign $-$ if and only if $n < 0$
the positive sign $+$ (or omitted) if and only if $n > 0$

If $n = 0$, then $n$ is represented simply as $0$.

## Also known as

Informally, we can say $n$ is (written) in base $b$ or to base $b$..