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

$${\left( {1217} \right)_8}$$ is equivalent to

$${73_x}$$ (in base $$-$$ $$x$$ number system) is equal to $${54_y}$$ (in base $$-y$$ number system), the possible values of $$x$$ and $$y$$ are