A trafic metering system for controlling the release of trafic from an entrance ramp onto a superhighway has the following speciications for a part of its controller. There are three parallel metering lanes, each with its own stop (red)–go (green) light. One of these lanes, the car pool lane, is given priority for a green light over the other two lanes. Otherwise, a “round robin” scheme in which the green lights alternate is used for the other two (left and right) lanes. The part of the controller that determines which light is to be green (rather than red) is to be designed. The speciications for the controller follow:

Inputs

PS Car pool lane sensor (car present—1; car absent—0)
LS Left lane sensor (car present—1; car absent—0)
RS Right lane sensor (car present—1; car absent—0)
RR Round robin signal (select left—1; select right—0)

Outputs

PL Car pool lane light (green—1; red—0)
LL Left lane light (green—1; red—0)
RL Right lane light (green—1; red—0)

Operation

1. If there is a car in the car pool lane, PL is 1.

2. If there are no cars in the car pool lane and the right lane, and there is a car in the left lane, LL is 1.

3. If there are no cars in the car pool lane and in the left lane, and there is a car in the right lane, RL is 1.

4. If there is no car in the car pool lane, there are cars in both the left and right lanes, and RR is 1, then LL = 1.

5. If there is no car in the car pool lane, there are cars in both the left and right lanes, and RR is 0, then RL = 1.

6. If any PL, LL, or RL is not speciied to be 1 above, then it has value 0.

(a) Find the truth table for the controller part.

(b) Find a minimum multiple-level gate implementation with minimum gate-input cost using AND gates, OR gates, and inverters.