$1)$ 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.

Design Constraints:

$($Note: Every time you cannot meet one of the constraints you may lose a few points.$)$

$1.$ Try not to use more than $4$ Flip$-$Flops of any type.

$2.$ Try to minimize the discrete gate count. State what you did in order to minimize the gate count.

$3.$ The system can be a single FSM or use any number of subsystems $($for example one subsystem for each sequence to be detected$).$

$4.$ You may use more Flip Flops, if needed, when providing alternative design solutions. In such case discuss pros and cons.

$5.$ Recall that no overlap is allowed when detecting $000$ twice.

$6.$ You can use Moore or Mealy FSMs$.$