(Solved): 1. [1] Design a Finite State Machine (FSM) to control the traffic lights at an intersection of a no ...

1. [1] Design a Finite State Machine (FSM) to control the traffic lights at an intersection of a north-south road with an east-west road, as shown in the illustration below. The FSM takes an input carew that indicates that a car is waiting on the east-west road. The FSM takes a second input, rst, that resets the FSM to a known state. There are six lights to control, green, yellow, and red, for both the north-south road and the east-west road. Consequently, the FSM outputs six control signals, one for each of the lights. An English-language description of the FSM is given below: (1) Reset to a state where the light is green in the NS direction and red in the EW direction. (2) When a car is detected in the EW direction (carew = 1), go through a sequence that makes the light go green in the EW direction and then return to green in the NS direction (3) A direction with a green light must first transition to a state where the light is yellow before going to a state where the light goes red. (4) A direction can have a green light only if the light in the other direction is red. Draw the state diagram for an FSM that controls the traffic lights. (Note: This is the exercise that we completed in class). 2. [1] Modify the traffic-light controller FSM (from problem 1) so that it makes lights go red in both directions for one clock cycle before tuming a light green. Draw the state diagram. 3. [1] Modify the traffic-light controller FSM (from problem 1) so that it takes an additional input, carns, that indicates when there is a car waiting in the NS direction. Change the logic so that, once the light has changed to EW, it stays with EW green until a car waiting in the NS direction is detected. Draw the state diagram. 4. [1] Design a Finite State Machine (FSM) to control a basic vending machine. The machine vends a single \( \$ 0.25 \) item and accepts only nickels \( (\$ 0.05) \) and dimes \( (\$ 0.10) \). The input signals are nickel and dime, and the outputs are vend and change. The two input signals go high when a nickel or dime is inserted into the machine (only one will be high at a time). When enough money has been added, the vend signal goes high for a single clock cycle. If \( \$ 0.30 \) has been inserted, change will also go high for one clock cycle. After vending an item, the FSM retums to the initial state where no money has been inserted. Draw the state diagram for an FSM that controls a basic vending machine. 5. [2] Consider the traffic light controller designed in problem 3. Implement the FSM as a synchronous sequential logic circuit. - Choose the Binary Code state assignment (i.e. 00, 01, 10, 11). - Show the state table / state assigned table. - Show K-maps for the next-state variables and output variables. - Derive expressions for the next-state logic and the output logic. - Draw the sequential logic circuit, including the combinational logic circuits for the nextstate and output, and the state register.