National qualifications curriculum support practical Electronics



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NATIONAL QUALIFICATIONS CURRICULUM SUPPORT

Practical Electronics


Circuit Design
Combinational Logic
[NATIONAL 5]

This advice and guidance has been produced to support the profession with the delivery of courses which are either new or which have aspects of significant change within the new national qualifications (NQ) framework.

The advice and guidance provides suggestions on approaches to learning and teaching. Practitioners are encouraged to draw on the materials for their own part of their continuing professional development in introducing new national qualifications in ways that match the needs of learners.

Practitioners should also refer to the course and unit specifications and support notes which have been issued by the Scottish Qualifications Authority.

http://www.sqa.org.uk/sqa/34714.html

Acknowledgement
© Crown copyright 2012. You may re-use this information (excluding logos) free of charge in any format or medium, under the terms of the Open Government Licence. To view this licence, visit http://www.nationalarchives.gov.uk/doc/open-government-licence/ or e-mail: psi@nationalarchives.gsi.gov.uk.

Where we have identified any third party copyright information you will need to obtain permission from the copyright holders concerned.


Any enquiries regarding this document/publication should be sent to us at enquiries@educationscotland.gov.uk.

This document is also available from our website at www.educationscotland.gov.uk.


Contents

Teaching and learning approaches 4
Basic logic functions 8
Combinational logic circuits 40
Converting logic circuits to Boolean expressions and truth tables 52
Converting Boolean expressions to logic circuits 63
Converting truth tables to logic circuits 70
Introduction'>Appendix 1 81

Teaching and learning approaches
Introduction
This guide provides suggestions, ideas and activities for practitioners on the delivery of combinational logic, which forms one learning outcome of the Circuit Design unit in National 5 Practical Electronics.
The content also covers all the combinational logic topics required in Circuit Design at National 4 so this guide can also be used for this level but this will require more tutorial exercises to be developed.

Aims and objectives
This guidance is intended to support the practitioner in the delivery Practical Electronics: Circuit Design, Combinational Logic.

The materials provide guidance on the following three parts:


1. basic logic functions

2. converting truth tables to logic circuits and converting Boolean expressions to logic circuits

3. converting logic circuits to Boolean expressions.
Learners could be encouraged to work through the exercises both individually and in pairs.
Once the basic concepts have been learned, simulation packages and logic tutor boards could be used to enhance the learning and provide practical hands-on experience.
The guidance will support practitioners in giving the learners the opportunity to gain an understanding of the basic gates used in combinational logic, their truth tables and Boolean expression.
They could also be able to convert truth tables and Boolean expressions to logic circuits and convert logic circuits to Boolean expressions.

Introduction
The first part of the advice and guidance covers the basic logic gates and provides the ANSI 2 and the BS EN 60617 logic symbols, truth table and Boolean expression for each gate.
The second part describes how truth tables and Boolean expressions are converted into logic circuits.
The third part describes how logic circuits are converted into Boolean expressions.
Learners sometimes cannot see the relevance to real-life situations of combinational logic, so practitioners may make reference to how logic is used everyday, ie ‘I will buy you a coffee – not’ is an example of the NOT or invert logic function.
Practical examples of where logic is used could also be included, eg:


  • Computers need combinational logic circuits to work.

  • Modern cars have electronic control units (ECUs). These are small, powerful computers that control various functions within the car, such as the fuel management system.

  • Televisions can have Freeview, which is a digital television signal that uses combinational logic.

Practitioners may wish to provide some other examples.



Suggested learning and teaching approaches
The skills and knowledge required will be gained as the learner progresses through each topic.
Monitoring progress
As each topic builds on the previous one, it is important that the learner is confident before moving on.
Learners therefore should be encouraged to take responsibility for their own progress so that they can work at their own pace and difficulties are identified as early as possible.
Suggested Learning and Teaching Approaches
These will be dependent on the facilities and expertise available in the centre but the following are suggested:


  • worked examples for each topic

  • tutorials to build up knowledge and understanding

  • learner-centred building and testing on simulation software

  • logic tutor-type boards individually and/or in pairs.



Resources
Some useful websites for basic combinational logic are:
http://www.play-hookey.com/digital/basic_gates.html

http://computer.howstuffworks.com/boolean1.htm

http://www.wisc-online.com/objects/ViewObject.aspx?ID=DIG1302

http://www.sci.brooklyn.cuny.edu/~goetz/projects/logic/combi.html

http://www.kpsec.freeuk.com/gates.htm
There are various software simulation packages available, such as Crocodile Clips, Electronic Workbench, MultiSim etc.
There are also a number of logic tutor systems available, for example the Feedback Logic tutor system.
It is suggested that learners use software simulation packages to build and test circuits. This is a safe method to use before they go on to use the more hands-on logic tutor systems.
Learners using simulation software can work either individually or in pairs. Circuits can be built and tested then saved. They can then be demonstrated at a later time.
The PowerPoint Presentation contains all the basic logic symbols and these can be used to make up further exercises if required.
Once the learners have gained experience using the simulation software, the circuits could be built and verified using logic tutor boards or whatever practical system the centre employs.
Because this is a practical learning environment, the relevant safety precautions must be observed.
A list of device numbers and pin connections for all the basic gates is provided in Appendix 1.
Basic logic functions
This section provides an introduction to the various logic gates AND, OR, NOT, XOR, NAND and NOR.
For each gate the logic symbol is provided along with the truth table and Boolean expression.
Both the ANSI 2 and the EN BS 60617 logic symbols are provided. However, after the tutorial questions in the first part of the document, only the ANSI 2 symbols will be used as they are more commonly used.
A short explanation of truth tables and Boolean algebra has also been included but will need further explanation or expanding during the lesson.
Learners often don’t understand where the logic 1s and 0s for the inputs come from. A short refresher on binary arithmetic might be appropriate here so learners understand how to count from 0 to 3 and 0 to 7 in binary.
Another method sometimes used is to take the value of the binary column, 8, 4, 2, 1 etc, to determine the number of 0s then 1s together, ie starting from the top, the 8 column will have eight 0s followed by eight 1s, the 4 column will have four 0s followed by four 1s etc.
This is an easy method for producing the truth tables and allows the learner to concentrate on the output of the table rather than how to produce the input values.
In order to aid the learner’s understanding, the concept for each logic gate, where possible, has been introduced using a simple electrical circuit using switches as the inputs and a light as the output. It would be beneficial to the learner if, during teaching, more examples could be given so reinforcing the idea that logic is used in all sorts of areas.
For example, a two-way lighting circuit used on staircases with one switch at the top and one at the bottom is an example of the XOR function.
The PowerPoint Presentation contains all the logic symbols used in these notes and these can be used to develop more tutorial exercises if required.
An internet search will provide a number of examples of simple uses of combinational logic circuits.
After the learners have gone through the tutorial exercises, the basic logic functions should be reinforced using simulation software such as Electronic workbench, MultiSim or whatever software package the centre uses to test logic functions.
This will provide added value to the learner’s knowledge.

Tutorial


  1. Identify the logic gate from the logic symbol



AND OR



NOT XOR



NOR NAND


AND XOR



OR NAND


Learners could also be asked to write the Boolean expression for each gate.


  1. Draw the logic gate and write the Boolean expression described by the following truth tables.




B

A

O/P




B

A

O/P

0

0

0




0

0

0

0

1

1




0

1

1

1

0

1




1

0

1

1

1

0




1

1

1

XOR OR


XOR logic symbol OR logic symbol
O/P = A B O/P = A + B



B

A

O/P




B

A

O/P

0

0

0




0

0

1

0

1

0




0

1

1

1

0

0




1

0

1

1

1

1




1

1

0

AND NAND

AND logic symbol NAND logic symbol

___

O/P = A.B O/P = A.B





B

A

O/P




A

O/P

0

0

1




0

0

0

1

0




1

1

1

0

0










1

1

0










NOR NOT


NOR logic symbol NOT logic symbol

____ _


O/P = A + B O/P = A

3. Determine the logic function represented by the following Boolean expressions:

_

O/P = P O/P = A.B.C


NOT AND

___


O/P = P + Q O/P = A.B
OR NAND

_____


O/P = A + B O/P = P Q
NOR XOR
Learners could also be asked to produce the truth table for each expression.

Converting from truth tables to logic circuits
This section builds on the knowledge of the basic gates by first taking the truth table and explaining that only lines on the truth table where the output is a logic 1 are required to design the logic circuit. This is because the circuit has to produce a logic 1 output for only these input conditions.
It could be highlighted that the inputs to the circuit are tied together on a truth table by the Boolean AND function. It could also be mentioned, that this AND function is called the ‘product of sums’ form.
Following on from this, all the lines on a truth table that have a logic 1 output are tied to each other by the Boolean OR function. This is called the ‘sum of products’ form. Boolean expressions produced from a truth table will always be in the sum of products form.
The practitioner could emphasise the following:


  • Because the circuit has only one output, there can only be one logic gate producing this output. Because the Boolean expression is in the sum of products form, the output gate will be an OR gate if more than one line on the truth table is a logic 1. However, if only one line on the truth table is a logic 1 then the output gate will be an AND gate.




  • The number of product terms, ie the number of lines on the truth table whose output is logic 1, also determines how many inputs there will be into the output gate.




  • It doesn’t matter what order the inputs are written in: A.B.C is exactly the same as C.A.B or B.C.A.




  • A + B + C is the also same as B + A + C etc.

Practitioners should emphasise to learners that any type of electrical circuit diagram flows from left to right on the page, ie signals input on the left and output on the right. Also, when drawing logic circuits or any kind of electrical diagram, wiring must always be drawn either horizontally or vertically, never at an angle.
Once the learners have progressed through the course the circuits could then be constructed and tested first using a simulation package, then with a logic tutor.
When using the logic tutor system, learners should be instructed to always connect all unused inputs to logic 1. This prevents problems occurring and is also good practice.
Example
Design a logic circuit for the following truth table.


R

P

Q

O/P

0

0

0

0

0

0

1

0

0

1

0

0

0

1

1

1

1

0

0

0

1

0

1

1

1

1

0

0

1

1

1

0

_ _


The two lines that have the output at logic 1 are R.P.Q and R.P.Q.

These are the two products of sum expressions.


_ _

The output is therefore O/P = R.P.Q + R.P.Q


_

The output gate is an OR gate with two inputs. One input is R.P.Q and the other is R.P.Q.


The circuit can now be built up from the output gate back to the input.
Although the complete logic circuit is shown below, it should be built up in stages from the output gate back to demonstrate how it is constructed.



Tutorial: Logic circuits from truth tables
Draw the logic circuit described by the truth tables below:
1.

B

A

O/P

0

0

0

0

1

0

1

0

0

1

1

1

AND truth table


O/P = A.B

2.


C

B

A

O/P

0

0

0

0

0

0

1

1

0

1

0

1

0

1

1

1

1

0

0

1

1

0

1

1

1

1

0

1

1

1

1

1

OR truth table


O/P = A + B + C

3.

B

A

O/P

0

0

0

0

1

1

1

0

1

1

1

0

O/P = A + B




4.

C

B

A

O/P

0

0

0

0

0

0

1

0

0

1

0

0

0

1

1

0

1

0

0

0

1

0

1

0

1

1

0

1

1

1

1

0

_

O/P = A.B.C


5.


C

B

A

O/P

0

0

0

0

0

0

1

1

0

1

0

0

0

1

1

0

1

0

0

0

1

0

1

0

1

1

0

0

1

1

1

0

_ _

O/P = A.B.C



6.

C

B

A

O/P

0

0

0

1

0

0

1

0

0

1

0

0

0

1

1

0

1

0

0

0

1

0

1

0

1

1

0

0

1

1

1

0

_ _ _


O/P = A.B.C


By looking at the truth table it can be seen that it is for a three-input NOR gate and could have been written as:

It should be pointed out that both circuits are correct but the NAND gate is used in a practical circuit as it uses fewer devices.
Although it is not part of this course, the above diagram illustrates one of De Morgan’s theorems in a practical circuit, ie move the inversion(s) from the input to the output and change the gate from AND to OR.
7.

C

B

A

O/P

0

0

0

0

0

0

1

0

0

1

0

1

0

1

1

0

1

0

0

0

1

0

1

0

1

1

0

0

1

1

1

1

_ _

O/P = A.B.C + A.B.C



8.


C

B

A

O/P

0

0

0

0

0

0

1

0

0

1

0

0

0

1

1

1

1

0

0

1

1

0

1

0

1

1

0

0

1

1

1

0

_ _ _

O/P = A.B.C + A.B.C




9.


C

B

A

O/P

0

0

0

0

0

0

1

1

0

1

0

0

0

1

1

0

1

0

0

0

1

0

1

0

1

1

0

1

1

1

1

0

_ _ _


O/P = A.B.C + A.B.C

10.


R

Q

P

O/P

0

0

0

1

0

0

1

1

0

1

0

1

0

1

1

1

1

0

0

1

1

0

1

1

1

1

0

1

1

1

1

0

_____


O/P = A.B.C
Note: It might be advisable to tell the learners to look closely at the truth table before designing the logic circuit.

11.

Z

Y

X

O/P

0

0

0

0

0

0

1

1

0

1

0

1

0

1

1

0

1

0

0

1

1

0

1

0

1

1

0

0

1

1

1

0

_ _ _ _ _ _

O/P = X.Y.Z + X.Y.Z + X.Y.Z


12.


C

B

A

O/P

0

0

0

0

0

0

1

0

0

1

0

0

0

1

1

1

1

0

0

0

1

0

1

1

1

1

0

1

1

1

1

0

_ _ _


O/P = A.B.C + A.B.C + A.B.C




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