Consider the equation $${\left( {123} \right)_5} = {\left( {x8} \right)_y}$$ with $$x$$ and $$y$$ as unknown. The number of possible solutions is _________.

The base (or radix) of the number system such that the following equation holds is __________
$${{312} \over {20}} = 13.1$$

The smallest integer that can be represented by an $$8$$-bit number in $$2's$$ complement form is

$$P$$ is a $$16$$-bit signed integer. The $$2's$$ complement representtation of $$P$$ is $${\left( {F87B} \right)_{16}}$$ . The $$2's$$ complement representation of $$8{}^ * \,P$$ is