Design a simple vending machine controller. The vending machine will sell bottles of water for $75$ cents. Customers can enter either a dollar bill or quarters. Once enough money is entered, the vending machine will dispense a bottle of water. If the user entered a dollar, it will return one quarter in change. A "money receiver" detects when money has been entered. The receiver sends two logic signals to our circuit indicating whether a dollar bill or quarter was received. $\backslash ($ A $\backslash )$ "bottle dispenser" system holds the water bottles and will release one bottle when its input signal is asserted. A "coin return" system holds quarters for change and will release one quarter when its input signal simultaneously or if a dollar is entered once the user has started entering quarters. Use Mealy FSM$,$ binary state encoding and D Flip$-$flops. $(20$ points$)$

a$)$ Draw the state diagram

b$)$ Create the state transition table

c$)$ Derive the next state logic and combinational logic