Using T$-$FFs$,$ design a $3-$bit register $[$C$,$B$,$A$]$ with a single input control x$.$ If x$=1,$ the register shifts the value of the memory units to the right. If x$=0,$ the register shifts them to the left. In shift right, $0$ enters C$.$ In shift left, $0$ enters A$.$ For instance: x$=1$: $011001,$ x$=0$: $011110.$ a$.[5$ marks$]$ Draw the state diagram of the circuit b$.[5$ marks$]$ Derive the state table c$.[10$ marks$]$ Draw the minimized logic diagram of the circuit