1. (Flip-Flops) The characteristic equations for a D flip-flop determine that the output Q is updated to either 0 or 1 after each clock cycle. A loadable D flip-flop has one additional input Load that allows data to be stored in the flip-flop for more than a single clock cycle. Design a loadable D flip-flop with an active low input Load using a normal D flip-flop and some combinational logic. Use the characteristic equations for a D flop-flop as a starting point. When the input signal Load=0, the flip-flop functions as a normal D flip-flop. When the input signal Load=1, the output Q stays at its previous value. 2. (Flip-Flops) Any flip-flop type can be implemented from another type with suitable logic applied to the latters inputs. Show how to implement the loadable D flip-flop of the previous problem starting with a T flip-flop. 3. (Sequential Circuit Design) The state diagram and block diagram of a vending machine is shown below. The vending machine is a sequential circuit that has 3 inputs and 5 outputs. The three inputs, (N,D, and Q) denote the next coin that has been deposited. (Only one coin can be deposited at a time!) The output (DC) denotes when the candy should be dispensed. The other outputs (C5,C10,C15, and C20) denote the amount of change that is to be returned to the customer. For the following sequence of inputs, list the states that are entered in their order and the value of each output. Assume that the machine starts in the reset state (start). a. 4 nickels are input. b. one dime and a quarter are entered. c. one nickel followed by two dimes. d. one nickel followed by one quarter. 4. (State Assignment) a. What is the minimum number of bits/flip-flops that can be used to allow each state to have a unique encoding for the vending machine presented in Figure 3? b. Write a sample state assignment that could be used for the vending machine. c. How many unique state assignments are there? Attempt to discuss the difference in hardware required when selecting between two state assignments that are complements of one another. d. One hot encoding is uses N bits to encode N states, where one and only one bit is true in each state. Show a one-hot encoding state assignment for the vending machine presented in the previous problem. 5. (State Diagrams) The vending machine shown in Figure 3 has three possible inputs. (N,D, and Q) corresponding to a nickel, dime and quarter. A modern vending machine, to be used in this problem, takes quarters and dollars only. This machine dispenses a single product, (some sort of candy) that costs 65 cents. a. Draw the block diagram for this circuit. Discuss your output encoding, that is, discuss how you distinguish between no change, vending a product, and all possible change values using the minimum number of binary outputs. b. Draw a state diagram for the modern vending machine. c. Show the state sequence and outputs that are produced when a person deposits three quarters. (Assume that the circuit starts in the reset state (start).)