The overall system to be implemented is a controller for a set of traffic lights at a crossroads, where one road runs north-south, and the other runs east-west. The controller in its simplest form is just a counter. Consider, for example, a single set of lights. We can create a table to show the expected sequence of lights as follows: a. Design the traffic lights north-south, east-west system. Begin by working out the sequence of lights for both directions and construct a table similar to the one above, assuming a three bit counter CBA. The sequence of lights should start with red in both directions, then allow east-west traffic to flow, then north-south, and back to east-west. Safety should be maintained at all times (that is, if one set of lights is at red + amber, green or amber, then the other set should be at red). It is not acceptable to maintain the lights at red throughout! b. Write down the Boolean algebra sum-of-products expression for the North-south lights (NS-G, NS_A, NS_R). _C. Using the laws of Boolean Algebra simplify the expressions for NS_A and NS_R as far as you can, showing each major step that you take. The rule you are applying at each stp should be explicitly stated (e.g. using the numbering on slide 15 of SYS-L4-Boolean Algebra, "distributive law", " A+A=1,etc) d. Given the simplified expression of part c, convert the expressions for NS_G, NS_A and NS_R into NAND only form. Show your working as above. Draw the circuit. e. Usually, traffic lights allow the green lights to be held much longer than other elements of the sequence. Assume a 3-bit register NS. NS holds the controller state in which the north-south traffic lights should stay green. Design and draw a circuit which detects the NS controller state, "suspends" the controller in that state, and activates a timer which counts down from a specified value. You may assume the circuitry to preload the timer with that value exists: you just need to activate the timer and detect when it is finished. When the timer is finished you should "resume" the controller sequence. Draw the registers, counter (controller sequence) and timer as black boxes: you do not need to implement those. Do this only for the NS lights