Design a sequential circuit that could be used in a vending machine. Suppose that a coin-operated vending machine dispenses candy under the following conditions: The machine accepts nickels and dimes. It takes 15 cents for a piece of candy to be released from the machine. If 20 cents is deposited, the machine will not return the change, but it will credit the buyer with 5 cents and wait for the buyer to make a second purchase. a) Derive the initial state diagram for the above vending machine. b) Apply state minimization methods to minimize the number of states. If no state minimization is possible, prove that you have the state diagram with minimal number of states. c) Using S-map encoding method assign the optimal codes to the states. d) Realize the control/FSM using DFFs. e) Implement the design using schematics