The Massachusetts Bay Transportation Authority (MBTA) has just awarded you a contract to revamp the signaling system on its Green Line. You have decided upon the following basic approach: Each section of track will have a sensor to determine whether there is a train in that section and a signal with red, yellow, and green lights. You want the light in a track section to show red if there is a train in the very next section, yellow if there is no train in the next section but the section after that is occupied, and green otherwise. You decide to place a logic module, shown schematically below, under each section of track:
Tracks are one-way only, and trains move left to right relative to the track control module. The outputs $G, Y$, and $R$ should be a 1 to light the green, yellow, and red signals, respectively, for this section of track. The input $P$ is 1 if there is a train in this section. The signals $A_{\mathrm{i}}$ and $B_{\mathrm{i}}$ are received from the next section, and outputs $A_{\mathrm{o}}$ and $B_{\mathrm{o}}$ are passed back to the previous section. You may do with these what you like, but there are only two wires available, and you may not add more.
A. Design the logic for this box to implement the signaling function. Describe what use you have made of lines $A$ and $B$.
B. Under switches that merge two incoming tracks into one outgoing track, you will need to put a special kind of module:
This module operates like a regular track control module except that it signals red in the previous section (and yellow in the section before that) to trains coming from the direction the switch is not currently set to accept. The input $S$ is 1 if the switch is set straight, 0 if it is tumed. Give a logic diagram for this new module. You need not worry about logic modules for switches that split one incoming track into two outgoing tracks.