• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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

...read more.

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

...read more.

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.

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Core & Pure Mathematics essays

  1. Best shape for gutter and further alegbra - using Excel to solve some mathematical ...

    31 3.33333 3.33333 14.42935 The formulae to calculate the area of this cross section are given in Appendix 1. Triangular cross section(V shape) - Area = x () x () sin? A =w2 sin? By varying ? by 1�, where 0� is at the point of the two sides touching each other to make a straight line.

  2. Functions Coursework - A2 Maths

    The graph y=f(x) is shown: There are three visible roots to the equation. I will take an approximate root for the root in interval [2,3] to be 3. As I shall explain later, the Newton-Raphson iteration will hopefully converge to the root in interval [2,3].

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work