Definition:Hexadecimal Notation

Definition
Hexadecimal numbers are numbers expressed in base $16$ notation.

That is, every number $x \in \R$ is expressed in the form:
 * $\displaystyle x = \sum_{j \mathop \in \Z} r_j 16^j$

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

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 doesn't look as good in proportional font.

Hexadecimal numbers, like binary numbers, have particular relevance in the field of computer science.

In that context, a number is usually indicated as being hexadecimal by subscripting $\mathrm H$ or $\mathrm h$ rather than $16$.

That is, $\mathrm{FFFF}_{16}$ would be rendered $\mathrm{FFFF_H}$ or $\mathrm{ffff_h}$, and so forth.