$(20$ points$)$ Design a minimized state diagram for a sequential circuit of a vending machine

controller. One product, a $$0\mathrm{.}35$ bottle of water $($output $W).$ The vending machine takes only

quarters $($input Q$)$ and dimes $($input D$),$ but refunds nickels $($output C$).$ No other I$/$O signals,

and it uses only a single register $(R$ for memory$).$ Show the complete state diagram and

state transition table.