ECE $233-$ Intro to Digital Systems

Design a sequential circuit for a finite state machine that detects the two binary input sequences $"00"$ and $"01."$ The patterns can overlap. For example, the sequence $001$ would output a $"1"$ twice $($once after $00$ and again after the last $1$ since it detected $"01.").$ The finite state machine has one input $(A)$ and one Moore output $(Y).(8$ points$)$

a$)$ Start by drawing the state diagram. $(3$ Points$)$