Design a $4-$bit binary modulo counter $($ mod$11$ using falling$-$edge triggered D flip$-$flops. $(25$ pts$)$

$($Example sequence for $4-$bit binary counter modulo $11($in decimal format$)$:

$\frac{0}{1}\frac{?}{?}\frac{2}{3}\frac{?}{?}\frac{4}{5}\frac{?}{?}\frac{6}{7}\frac{?}{?}\frac{8}{9}\frac{?}{?}\frac{10}{0}\frac{?}{?}\frac{1}{2}\frac{?}{?}\frac{3}{4}\frac{?}{?}\frac{5}{6}\frac{?}{7\text{d}\text{o}\text{t}\text{s}}$