Question $3(15$ m$)$

The picture below shows the intersection of a road. Some vehicle detection sensors are placed along lanes C and D $($main road$)$ and lanes A and B $($access road$).$ These sensors$"$ outputs are LOW $(0)$ when no vehicle is present and HIGH $(1)$ when a vehicle is present. The intersection traffic light is to be controlled according to the following logic: The east$-$west $($E$-$W$)$ traffic light will be green whenever both lanes $C$ and $D$ are occupied.

The $E-W$ light will be green whenever either $C$ or $D$ is occupied but lanes A and $B$ are not both occupied.

The N$-$S light will also be green whenever both lanes A and $B$ are occupied but $C$ and $D$ are not both occupied.

The N$-$S light will also be green when either $A$ or $B$ is occupied while $C$ and $D$ are both vacant.

The E$-$W light will be green when no vehicles are present.

Using the sensor outputs A$,$ B$,$ C and D as inputs, design a logic circuit to control the traffic light. There should be two outputs$-$S and E$-$W that go HIGH when the corresponding light is to be green. Simplify the circuit as much as possible and show all steps.