$1)$ On startup we look at detecting the sequence $000$ first and then $000$ again $($no overlap allowed$).$

$2)$ After the leading sequence $(000)$ is detected twice $($not necessarily consecutively$),$ without overlap, we ignore subsequent instances of $000$s and look to detect the sequence $111$ once.

$3)$ After a sequence $111$ is detected once, we ignore subsequent instances of $111$s and look again to detect the sequence $000$ twice. The process continues alternating between the detection of the $000$ sequence twice and then the $111$ sequence once.

$4)$ The timing trace shown below depicts a possible example, using Moore, depicting some detections events in order to clarify the prescribed functionality for this FSM$.$

$5)$ If possible, provide alternative design solutions stating any trade$-$offs among them.

$6)$ Use LogiSim to verify, and demonstrate to the instructor, that your design works as intended.

X $10000011101111000111110000000111$

Z $000010000000000001001000010010001$