Definition:Hexadecimal Notation

Definition
Hexadecimal notation is the technique of expressing numbers in base $16$.

Every number $x \in \R$ is expressed in the form:
 * $\ds x = \sum_{j \mathop \in \Z} r_j 16^j$

where:
 * $\forall j \in \Z: r_j \in \set {0, 1, \ldots, 15}$

In order to be able to represent numbers in such a format conveniently and readably, it is necessary to render the digits $10$ to $15$ using single characters.

The convention is for the following:

Thus $\mathrm{FFFF}_{16} = 15 \times 16^3 + 15 \times 16^2 + 15 \times 16 + 15 = 65\,535_{10}$.

Their lowercase renditions can equally well be used, e.g. $\mathrm{ffff}_{16} = 65\,535_{10}$, but it does not look as good in proportional font.

Also known as
Hexadecimal notation can also be referred to as hexadecimal representation.

The abbreviation hex is common, particularly in the field of computer science.