The figure below represents an intersection of two streets. Sensors have been placed in the proximity of the intersectio

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The figure below represents an intersection of two streets. Sensors have been placed in the proximity of the intersection, along A, B, C and D lanes to detect vehicles' presence. A sensor's output is 1 when there is no vehicle on its monitored lane (indicated as free in the following) and 0 when a vehicle is present (busy lane). The two sets of intersection lights (East-West or EW, and North-South or NS) observe the following logic:
1) The EW lights will turn green when vehicles will be simultaneously detected on both C and D lanes.2) The EW lights will also be green when either C is busy or D is busy, and, if A and B are not both busy at the same time.3) The NS lights will be green when vehicles will be sensed on both A and B lanes, and, if C and D are not simultaneously busy.4) The NS lights will also turn green when either A is busy or B is busy, but C and D are both free.5) The EW lights will also be green when no vehicle is present in the intersection.
a) Using sensors A, B, C, D as input variables, implement a logical combinational circuit that controls the lights. There will be 2 output functions NS(A,B,C,D) and EW(A,B,C,D) whose values will be 1 when the light is green (and 0 for the red!). Simplify the 2 functions and derive their Sum-of-Products minimal form (no logic diagram asked).b) Realize NS(A,B,C,D) and EW(A,B,C,D) using a 4-to-16 decoder and 2 OR gates; draw the circuit diagram.