\begin{definition}[Definition:Basis Expansion/Negative Real Numbers]
Let $x \in \R: x < 0$.
We take the absolute value $y$ of $x$, that is:
:$y = \size x$
Then we take the '''expansion of $y$ in base $b$''':
:$\size {s . d_1 d_2 d_3 \ldots}_b$
where $s = \floor y$.
Finally, the '''expansion of $x$ in base $b$''' is defined as:
:$-\sqbrk {s . d_1 d_2 d_3 \ldots}_b$
\end{definition}