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:
 * $$x = \sum_{j \in \Z} r_j 16^j$$

where $$\forall j \in \Z: j \in \left\{{0, 15}\right\}$$.

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.