\begin{definition}[Definition:Hexadecimal Notation]
'''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:
{{begin-eqn}}
{{eqn | l = 10
      | o = :
      | r = \mathrm A
}}
{{eqn | l = 11
      | o = :
      | r = \mathrm B
}}
{{eqn | l = 12
      | o = :
      | r = \mathrm C
}}
{{eqn | l = 13
      | o = :
      | r = \mathrm D
}}
{{eqn | l = 14
      | o = :
      | r = \mathrm E
}}
{{eqn | l = 15
      | o = :
      | r = \mathrm F
}}
{{end-eqn}}
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.
\end{definition}