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 $b \in \Z$ be an 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 $b$.