Problem $3(40$ points$).$

Design an FSM with one input, A$,$ and two outputs, X and Y $.$

X should be $1$ if A has been $1$ at least two times altogether AND the most recent value of A was $0,$ and $0$ otherwise. In other words, once A has been $1$ for $2$ times total, X will be only be $1$ when A is $0.$

Y should be $0$ if A has been $1$ for the last two consecutive inputs, and $1$ otherwise. In other words, Y needs to constantly check on what the inputs are, going back to outputting a $1$ when needed.

a$)$ Draw the state transition diagrams. You may choose either a Moore or Mealy machine. It is easiest to model this as one diagram per output!

b$)$ Using binary encodings, complete a full state transition table for each diagram.

c$)$ Using binary encodings, complete an output table for each diagram.

d$)$ Write Boolean equations for the next state and output for each diagram.