Definition:Basis Expansion/Negative Real Numbers

Definition
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:
 * $-\sqbrk {s . d_1 d_2 d_3 \ldots}_b$