Definition:Basis Expansion/Negative Real Numbers

Definition
Let $x \in \R: x < 0$.

We take the absolute value $y$ of $x$, i.e. $y = \left|{x}\right|$.

Then we take the expansion of $y$ in base $b$:
 * $\left[{s . d_1 d_2 d_3 \ldots}\right]_b$

where $s = \left \lfloor {y} \right \rfloor$.

Finally, the expansion of $x$ in base $b$ is defined as:
 * $-\left[{s . d_1 d_2 d_3 \ldots}\right]_b$