Draw the state diagram for a state machine that detects the sequence $1001$ from an incoming stream of bits. There is just a single input. Be sure to draw all the arrows. The state machine should have an INIT$($ialize$)$ state that can be entered with a 'reset' signal.

The output of the state machine should output $F=1$ if the sequence is Found and $F=0$ if the sequence is not found. $F=1$ can be output more than once $($the machine is always running and looking for $\text{'}1001\text{'})$

At first, you named your states. Now encode them into digital numbers. How many bits $($flip$-$flops$)$ are needed?

What is the minimum number of clock periods between two observations of the output going high $(F=1)?$