$4)$ Design a sequential circuit for a finite state machine that detects the two binary input sequences $"01"$ and $"11."$ The patterns can overlap. For example, the sequence $011$ would output a $"1"$ twice $($once after $01$ and again after the last $1$ since it detected $"11.").$ The finite state machine has one input $($A$)$ and one Moore output $($Y$).(8$ points$)$

a$)$ Start by drawing the state diagram. Apply state minimization to end up with four states only. $(3$ Points$)$