# Category:Definitions/Number Bases

This category contains definitions related to Number Bases.
Related results can be found in Category:Number Bases.

Let $n \in \Z$ be an integer.

Let $b$ be any integer such that $b > 1$.

By the Basis Representation Theorem, $n$ can be expressed uniquely in the form:

$\ds n = \sum_{j \mathop = 0}^m r_j b^j$

where:

$m$ is such that $b^m \le n < b^{m + 1}$
all the $r_j$ are such that $0 \le r_j < b$.

The number $b$ is known as the number base to which $n$ is represented.

$n$ is thus described as being (written) in base $b$.

Thus we can write $\ds n = \sum_{j \mathop = 0}^m {r_j b^j}$ as:

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

or, if the context is clear:

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

## Subcategories

This category has the following 5 subcategories, out of 5 total.

## Pages in category "Definitions/Number Bases"

The following 25 pages are in this category, out of 25 total.