$(10$ pts$)$ Design a stream analyser that attempts to detect a certain key in a stream of bits.

Create a Moore finite state machine that accepts only $1$ bit as an input every cycle and detects

the sequence $1011.$ When the pattern is detected the output $(Z)$ should become $1$ in the next

cycle. $Z$ should be $0$ in every other cycle. Make sure this state machine can detect nested

instances of the key $($e$.$g $1011011$ should set $Z=1$ on the $4$ th and $7$th cycle$).$

a$.(4$ pts$)$ Draw the Moore state machine for this input sequence pattern recogniser.