Design a synchronous sequential machine with external synchronization which states are coded on \(4\) bits \(q_3 q_2 q_1 q_0\) whose table is the following:

\(

\begin{tabular}{|c|c|c|c|c|c|c|c|}

\hline

q_3 & q_2 & q_1 & q_0 & q_3' & q_2' & q_1' & q_0' \\

\hline

\hline

0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\

\hline

0 & 0 & 0 & 1 & 0 & 0 & 1 & 0 \\

\hline

0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 \\

\hline

0 & 0 & 1 & 1 & - & - & - & - \\

\hline

\hline

0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 \\

\hline

0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 \\

\hline

0 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\

\hline

0 & 1 & 1 & 1 & - & - & - & - \\

\hline

\hline

1 & 0 & 0 & 0 & 1 & 0 & 0 & 1 \\

\hline

1 & 0 & 0 & 1 & 1 & 0 & 1 & 0 \\

\hline

1 & 0 & 1 & 0 & 1 & 1 & 0 & 0 \\

\hline

1 & 0 & 1 & 1 & - & - & - & - \\

\hline

\hline

1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 \\

\hline

1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 \\

\hline

1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\

\hline

1 & 1 & 1 & 1 & - & - & - & - \\

\hline

\end{tabular}

\)

a) Draw the correspondent state diagram.

b) Design the machine using Flip-Flop D.

What I'm not sure of is the point "a". Is the diagram I've done correct? Or I missed something?