Problem $9$:

A student just learned how a two$-$bit synchronous binary counter works, and he is excited about building his own. He does so$,$ and the circuit works perfectly.

After that success, student tries to expand on their success by adding more flip$-$flops, following the same pattern as the two original flip$-$flops:

Unfortunately, this circuit didn't work. The sequence it generates is not a binary count. Determine what the counting sequence of this circuit is$,$ and then try to figure out what modifications would be required to make it count in a proper binary sequence.