A traffic light is installed at a junction of a railroad and aroad. The light is controlled by two switches in the rails placed 1mile apart on either side of the junction. A switch is turned onwhen the train is over it and is turned off otherwise. The traffic light changes from green (logic 0) to red (logic 1) when thebeginning of the train is 1 mile from the junction. The lightchanges back to green when the end of the train is 1 mile away fromthe junction. Assume that the length of the train is less than 2miles.

(a) Obtain a primitive flow table for the circuit.
(b) Show that the flow table can be reduced to four rows.