\begin{definition}[Definition:Binary Notation]
'''Binary notation''' is the technique of expressing numbers in base $2$.
That is, every number $x \in \R$ is expressed in the form:
:$\ds x = \sum_{j \mathop \in \Z} r_j 2^j$
where $\forall j \in \Z: r_j \in \set {0, 1}$.
\end{definition}