The idea behind state machines that recognise sequences is fairly simple. You only need 2 types of states for this state machine. The first is for 0s in the sequence and the other is for 1s. Each one has two transitions - if the input matches its recognition value then it transitions to the next state on the line, otherwise it transitions back to the first state. For each correct value receive it moves down one in the line. If it reaches the last state then you know the sequence is correct. If any value received is incorrect it resets the state machine and the sequence need to start over.
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