This problem concerns a traffic light placed on a stretch of road where there is no cross traffic, but where pedestrians often cross. There are two sets of lights, one facing each direction of traffic, and two pedestrian buttons, one on each side of the road. Pushing either button while the light is green causes the light to turn yellow for 10 seconds, then red for 120 seconds, and back to green. Pushing buttons while the light is yellow or while the light has been red for 10 seconds or less has no effect. Pushing a button while the light has less than 10 seconds to go before it turns green will cause the light to stay red for at least 10 seconds more than it would otherwise. We want to design a sequential circuit for the traffic light controller.

A. Show a state-transition diagram and a state-transition table for the traffic light. Let the input be the state of the buttons (1 if either button has been pushed, 0 otherwise), and assume that a clock pulse occurs once every 10 seconds. (In other words, no state transition can occur except at 10-second intervals; every 10 seconds, the input is examined and a state transition, if called for, is made.)

B. How many D flip-flops will you need to represent the states you have defined? Indicate the correspondence you have made between states in your answer to part A and the states of your set of D flip-flops. Show truth tables and Boolean equations describing the next state of each flip-flop, based on the current state of the circuit and any other appropriate inputs.

C. Draw the circuit. Assume that two input lines are available: a clock line, which gives a short pulse once every 10 seconds, and a button line, which is high if a button is pushed. Your circuit should have three output lines controlling the lights; label the lines "red," "yellow," and "green."

D. It would be nice if the pedestrian did not have to lean on the button until a transition occurred. Your circuit currently has this property, unless you have departed from the clocked sequential-machine synthesis procedure suggested in the previous steps and described in the text. Give a modification of your circuit that solves this problem, and explain why it works.