Answer
$256$
Work Step by Step
The Multiplication Rule says that if an event $e_1$ can be performed in $n_1$ ways and an event $e_2$ can be performed in $n_2$ ways, then there are $n_1n_2$ ways of performing them together. This can easily be extended to $n$ events.
Here we have $8$ digits each with $2$ possibilities ($0$ or $1$), so the number of possibilities is:
$2^8=256$
