Gray Code FSM a$.$ Draw a state diagram for an FSM with an input G and three outputs x$,$ y$,$ and z$.$ The xyz outputs generate the gray code sequence $000,010,011,001,101,111,110,100,$ repeat. The output should change only on a rising clock edge when the input G $=1.$ Make the initial state $000.(10$ pts$)$ b$.$ Create a truth table for this system. This should include the input, current state, next state, and outputs. $(10$pts$)$ c$.$ Create the controller circuit diagram for this system. $(10$pts$)$