A traffic light controller receives a 4-bit input that changes every 5 seconds. The input sequence is a simple counter that counts from binary 0 to binary 15 and then starts again from binary 0. These signals go to 4 outputs, NSH, NSL, EWH, EWL. The first two outputs NSH and NSL respectively represent the high and low bits that are fed to the lamps that face in the North-south direction. The other two outputs EWH and EWL respectively represent the high and low bits that are fed to the lamps that face in the East-West direction. The following table indicates how setting the high and low bits determines the color of the lamp: High Low Lamp Color
0 0 Green
0 1 Yellow
1 0 Red
1 1 REd
Each light should be green for 30 seconds, yellow for 5 seconds, and then red for 45 seconds. There should be two 5 second intervals when both lights are red. Assume that for the interval where the input is 0000, the North-South light has just turned green, and the East-West light has been red for 5 seconds already. Design the circuitry that feeds from ABCD to the two outputs. You may represent your answer as algebraic equations (make sure to simplify).