$2.$ Consider a state table for a finite state machine with $8$ states labeled $\backslash ($ A$,$ B$,\backslash$ldots$,$ H $\backslash ).$

a$)$ Find all equivalent states and show that an equivalent state machine can be implemented with four states and identifying how these states map to the original states. Give the final state table.

b$)$ implement the reduced state machine as a moore machine and sketch the resulting circuit all logic should be fully reduced.