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Design and construction of circuits to solve problems.

Extracts from this document...

Introduction

Design and construction of circuits to solve problems.

The Problem: The traffic department is to install a set of traffic lights at a set of crossroads to reduce the number of accidents. They have lost the plans for the circuit required to operate the traffic light at the crossroads. The traffic lights are the traditional English colours of Red, Amber and Green.

First of all I will need to construct a truth table to see the sequence of the lights

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Middle

1

1

0

1

1

0

1

0

0

0

0

1

1

1

1

1

0

0

0

1

0

From the Truth table above I can now create a Boolean equation for each time the red, amber and green light is on.

Traffic Light 1

       _  _  _     _  _            _  _        _                _

R = X·Y·Z + X·Y·Z + X·Y·Z + X·Y·Z + X·Y·Z + X·Y·Z

This is the Boolean equation for when the red light is on there are 6 states and a load of different gates which will cost far to much money and time so we can simplify this so we can use the least amount of gates possible to keep the cost down but not the time so if I create the Boolean equation for when the red light is off and the put a NOT gate after

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Conclusion

           _  

A1         = X·Z

           _     _

G1 = X·Y·Z (This equation cannot be simplified anymore.)

Traffic light 2

I have only applied De Morgan’s Theorem to the red light on traffic light 1, I will now need to do the same for the red light on traffic light 2.

De Morgan’s Theorem

            _

R2 = X·Y·Z + X·Y·Z

            _

R2 = X·Y·Z · X·Y·Z

        _    _   =   _   _   _

R2 = X+Y+Z · X+Y+Z

         _   _        _    _  _

R2 = X+Y+Z · X+Y+Z

I will now need to simplify this equation.

So now,

        _    _        _   _   _

R2 = X+Y+Z · X+Y+Z

         _     _

R2 = X + Y

             _

A2 = X·Y·Z + X·Y·Z

A2 = X·Z

                 _

G2 = X·Y·Z

Now I have all the equation I need to create my circuit.

Traffic Light 1

Traffic Light 2

                  _

R1 = X+Y

           _  

A1 = X·Z

           _     _

G1 = X·Y·Z

         _     _

R2 = X + Y

A2 = X·Z

                 _

G2 = X·Y·Z

Key:

_

? = image00.png

· = image01.png

+ = image02.png

Circuit

image03.png

...read more.

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