$6.[10$ points$]$ Implement a finite state machine that has the following behavior:

If the input is $1$ it outputs $4$ numbers from $00$ through $11$ in hops of $1$ with each tick of the clock. The next ouput after $11$ is $00$ and repeats its actions

If the input is $0,$ then the ouput starts increasing in hops of $2.$ So if the number shown on the output is $11$ then the output displayed next will be $01$ then $11$ again and so on$.$ Similarly if the number number shown is $00,$ then next output is $10$ and then $00$ again.

To answer this question completely you must give the

$-$ State transition graph $(2\mathrm{.}5$ points$)$

$-$ State transition table $(2\mathrm{.}5$ points$)$

$-$ Ouput table $(1$ point$)$

$-$ Circuit diagram $(4$ points$).$