Assume a sequential circuit that receives one bit binary input $(1$ or $0)$ at each clock. This circuit will output $1$ when it receives a signal with the sequence of $"0011."$ Otherwise, the output is $0.$ Design this circuit using an FSM and draw the resulting circuit from the FSM$.$ Show your work in detail along with the optimizations you performed.Use the variable x for input, y$1$y$2$ for state at time t$,$ Y$1$Y$2$ for state at time t$+1,$ and z for output.