$(15$ points$)$ Consider the synchronous circuit presented in the next figure. Assume the initial values in the FFs are zero.

b$)$ Trace the behavior of the FFs by completing the timing diagram for at least $7$ clock cycles.

c$)$ If fclk $=75MHz,$ what is the frequency and the duty cycle of the Q$1$ waveform?

d$)$ What is the name of this circuit? What is the counting sequence?

Q$1,0$

Q$20$

Q$30$