In general, an n$-$bit down counter can be constructed by

using the following equations.

$Q_0^{+}\frac{?}{b}=ar(Q_0)$

$Q_i^{+}=Q_{i}o+t_i(i1)$

where $t_i\frac{?}{b}=ar\frac{Q_{i-1}}{b}ar(Q_{i-2})cdot\frac{s}{b}ar(Q_0).$

Construct a $4-$bit down counter. Draw the circuit diagram.