Logic Systems Boolean Reduction Question

[DethRose]

Logic Systems Boolean Reduction Question!

Ok i received an assignment due on monday and have to idea how to get started...i am supposed to design a traffic light using the following criteria:

a) The east west (E-W) traffic light will be green whenever both lanes C and D are occupied.
b) The E-W light will be green whenever either C or D is occupied but lanes A and B are not
both occupied.
c) The north -south (N-S) light will be green whenever both lanes A and B are occupied but
C and D are not both occupied.
d) The N-S light will also be green when either A or B is occupied while C and D are both
vacant.
e) The E-W light will also 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, N-S and E-W, that go HIGH when the corresponding
light is green. Simplify the circuit as much as possible and show all steps!

I need to write an equation for each light set (e-w) and (n-s) but have no idea what they are. I think they may be:

N-S

[tex](ab)[/tex][tex]([/tex][tex]\overline c + \overline d[/tex][tex])[/tex][tex]+[/tex][tex](a+b)[/tex][tex]([/tex][tex]\overline c \overline d)[/tex]


E-W

[tex](cd)+(c+d)(\overline a[/tex][tex]+[/tex][tex]\overline b)[/tex][tex]+ \overline a[/tex][tex]\overline b[/tex][tex]\overline c[/tex][tex]\overline d[/tex]

 

[anathema]

Hi there! It sounds like you are being asked to create a logic circuit using Boolean reduction to control a traffic light. This can definitely seem overwhelming at first, but don't worry, I'm here to help you get started.

First, let's break down the criteria given into simpler terms. We have four inputs: A, B, C, and D. These inputs represent the sensors that detect whether there are vehicles in each lane. We also have two outputs: N-S and E-W. These outputs will control the corresponding traffic lights.

Now, let's look at each criterion and translate it into a logical statement:

a) The E-W light will be green whenever both lanes C and D are occupied.
This can be written as E-W = C AND D

b) The E-W light will be green whenever either C or D is occupied but lanes A and B are not both occupied.
This can be written as E-W = (C OR D) AND (NOT(A AND B))

c) The N-S light will be green whenever both lanes A and B are occupied but C and D are not both occupied.
This can be written as N-S = A AND B AND (NOT(C AND D))

d) The N-S light will also be green when either A or B is occupied while C and D are both vacant.
This can be written as N-S = (A OR B) AND (NOT(C OR D))

e) The E-W light will also be green when no vehicles are present.
This can be written as E-W = NOT(A OR B OR C OR D)

Now, we have five logical statements for each output. We can use Boolean reduction to simplify these statements and create a logic circuit. Here are the steps to do so:

1. Convert all statements into their corresponding Boolean expressions using the logical operators AND, OR, and NOT. For example, the first statement would be written as E-W = C AND D.

2. Use Boolean algebra rules to simplify the expressions. This may involve using De Morgan's laws, distributive property, and other simplification techniques. For example, the fourth statement can be simplified as N-S = (A OR B) AND (NOT(C AND D)) = (A OR B) AND (NOT(C) OR NOT(D)) = (A OR B) AND (NOT C OR NOT D).

3. Once you have simplified all the expressions, you can use Karnaugh maps to further simplify

 

[wais]

In response to your content, it seems like you have already made some progress on your assignment. It is important to first understand the criteria given and then break it down into logical statements or equations. From the given criteria, we can see that the E-W light will be green in three different scenarios: when both lanes C and D are occupied, when either lane C or D is occupied but not both, and when there are no vehicles present. Similarly, the N-S light will be green in two different scenarios: when both lanes A and B are occupied but not both C and D, and when either lane A or B is occupied while C and D are vacant.

Your equations for the lights seem to be correct based on the given criteria. It is important to simplify the equations as much as possible to reduce the number of components needed in the logic circuit. You can use Boolean algebra laws to simplify the equations further. For example, you can use the distributive law to simplify the first part of the E-W equation to (c + d)(a + b).

Once you have simplified the equations, you can then design the logic circuit using logic gates such as AND, OR, and NOT gates. You can use the simplified equations as the inputs for the gates and the outputs will be the N-S and E-W lights going HIGH when the corresponding light is green.

I would also suggest breaking down the circuit into smaller parts and testing each part separately before combining them together. This will help in identifying any errors and making necessary corrections.

Overall, it seems like you are on the right track and with some more effort and practice, you will be able to successfully design the traffic light using logic systems and Boolean reduction. Good luck with your assignment!