# Digital Electronic Engineering

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Digital Electronic Engineering

Name Class Teacher

Ellon Academy Technical Faculty

Learning Intentions

I will learn about TTL and CMOS families of IC's, being able to distinguish between them

I will be able to identify single logic gate symbols I will be able to complete Truth Tables for single logic gates and

combinational logic circuits I will learn to analyse and simplify combinational logic circuits I will learn what a Boolean expression is and how to write one for a

given logic circuit I will learn about NAND gates and I will be able to determine

equivalent circuits made from them I will learn to form circuits to given specification

Success Criteria

I can develop digital electronic control systems by: Designing and constructing complex combinational logic circuits Describing logic functions using Boolean operators Simplifying logic circuits using NAND equivalents Testing and evaluating combinational logic circuits against a specification

YENKA is a free program you can download at home to build electronic circuits and help you with your studies

http://www.yenka.com/en/Free_student_home_licences/

To access video clips that will help on this course go to www.youtube.com/MacBeathsTech

1

Switching Logic

Although it may not always seem like it, electronics and electronic systems are very logical in the way that they work. In the simplest form, if you want a light to come on, then you press a switch. Of course, it gets more complicated than that. Most technological systems involve making more complicated decisions: for example, sorting out bottles into different sizes, deciding whether a room has a burglar in it or not, or knowing when to turn a central heating system on or off. Logic gates are used in dealing with and processing a combination of different inputs. This switching logic can be applied to electrical switches and sensors, pneumatic valves or hydraulic systems. Switching logic uses logic gates to perform decisions. In National 5 you have already gained experience in the use of NOT, AND and OR logic gates.

http://goo.gl/yo2wOC

2

NAND logic gate

The NAND gate is effectively an inverted AND gate. In other words, the results obtained from the output are the opposite to those of the AND gate. This gate is often referred to as ‘NOT AND’. When drawing up the truth table for the NAND gate it can be difficult to ‘picture’ or imagine the results. The best way to do this is to pretend that it is an AND gate and then invert (reverse) the results, thus giving you the outputs for the NAND gate.

A Z

B

Symbol for NAND Gate

Task 1 Set up the E&L modular board electronic system and complete the NAND table using the system to confirm the outputs at Z.

Switc h Unit

Power Connec tion

Switc h Unit

Nand Gate

Transduc er

Bulb

d rive r

Unit

A

B

AND

Z

0

0

0

1

1

0

1

1

NAND Truth table

3

The NOR logic gate

The NOR gate is effectively an inverted OR gate. In other words, the results obtained from the output are the opposite to that of the OR gate. This gate is often referred to as ‘NOT OR’. As with the NAND gate, when drawing up the truth table for the NOR gate it can be difficult to ‘picture’ or imagine the results. The best way to do this is to pretend that it is an OR gate and then invert (reverse) the results, thus giving you the outputs for the NOR gate.

A Z

B

SYMBOL FOR NOR GATE Task 2 Using the E&L boards once more, build up this circuit to confirm how a NOR gate works, and complete the truth table.

Switc h Unit

Power Connec tion

Switc h Unit

Nor Gate

Transduc er

Bulb

d rive r

Unit

A

B

OR

Z

0

0

0

1

1

0

1The X1OR logic gate

NOR Truth table

4

The XOR Logic Gate

This IC sends out logic when only 1 OR the other is sending logic 1. It will not work if both signals are sending out logic 1 like a normal OR gate does. This is why a XOR gate is sometimes known as an ‘X-Treme OR’ or an ‘Exclusive OR’

Z

Symbol for XOR Gate

Task 3 Using Crocodile Technology, build up this circuit to confirm how a XOR gate works, and complete the truth table.

A

B

OR

Z

0

0

0

1

1

0

1

1

XOR Gate

XOR Truth table

http://goo.gl/4uQfaP

5

Task 4 For each of the following examples, state whether the output Z is at logic 0 or logic 1.

(a)

1 Z

1

(b)

1 Z

0

(c)

1

Z

(d) 1 Z 1

(e) 1 Z 0

(g) 1 1

(f) 1 Z 1

Z

(h) 1

0

Z 6

Boolean Expressions

Each logic gate has a corresponding Boolean mathematical formula or expression. The use of these expressions saves us having to draw symbol diagrams over and over again.

NOT

A

Z

AND

A B

Z

OR

A

B

Z

NAND

A B

Z

NOR

A B

Z

XOR

A A B

Z

7

Combinational Boolean

So far, we have only looked at simple logic systems. In reality, most logic systems use a combination of different types of logic gates. This is known as ‘Combinational Logic’. Boolean Expressions can be worked out from these to know the equation for the circuit..

Example

A

B

Z

C

To work this out you have to take it one step at a time and work out the equation as it goes through each logic gate.

1. A A

B

Z

C

You can find out that the line for A soon turns into A

2. A

B C

A

A+B

Z

The lines for A and B now changes at it goes through the next logic gate.

3. A

B C

A

A+B

Z (A+B) .C

As we progress through the circuit we can now add C.

Z = . (A+B) C

8

Task 5 Work out the Boolean Expression for each of the following a)

A Z

B

b) A

B Z

C

c)

A B

C D

d) A

B

C

Z Z

9

Name Class Teacher

Ellon Academy Technical Faculty

Learning Intentions

I will learn about TTL and CMOS families of IC's, being able to distinguish between them

I will be able to identify single logic gate symbols I will be able to complete Truth Tables for single logic gates and

combinational logic circuits I will learn to analyse and simplify combinational logic circuits I will learn what a Boolean expression is and how to write one for a

given logic circuit I will learn about NAND gates and I will be able to determine

equivalent circuits made from them I will learn to form circuits to given specification

Success Criteria

I can develop digital electronic control systems by: Designing and constructing complex combinational logic circuits Describing logic functions using Boolean operators Simplifying logic circuits using NAND equivalents Testing and evaluating combinational logic circuits against a specification

YENKA is a free program you can download at home to build electronic circuits and help you with your studies

http://www.yenka.com/en/Free_student_home_licences/

To access video clips that will help on this course go to www.youtube.com/MacBeathsTech

1

Switching Logic

Although it may not always seem like it, electronics and electronic systems are very logical in the way that they work. In the simplest form, if you want a light to come on, then you press a switch. Of course, it gets more complicated than that. Most technological systems involve making more complicated decisions: for example, sorting out bottles into different sizes, deciding whether a room has a burglar in it or not, or knowing when to turn a central heating system on or off. Logic gates are used in dealing with and processing a combination of different inputs. This switching logic can be applied to electrical switches and sensors, pneumatic valves or hydraulic systems. Switching logic uses logic gates to perform decisions. In National 5 you have already gained experience in the use of NOT, AND and OR logic gates.

http://goo.gl/yo2wOC

2

NAND logic gate

The NAND gate is effectively an inverted AND gate. In other words, the results obtained from the output are the opposite to those of the AND gate. This gate is often referred to as ‘NOT AND’. When drawing up the truth table for the NAND gate it can be difficult to ‘picture’ or imagine the results. The best way to do this is to pretend that it is an AND gate and then invert (reverse) the results, thus giving you the outputs for the NAND gate.

A Z

B

Symbol for NAND Gate

Task 1 Set up the E&L modular board electronic system and complete the NAND table using the system to confirm the outputs at Z.

Switc h Unit

Power Connec tion

Switc h Unit

Nand Gate

Transduc er

Bulb

d rive r

Unit

A

B

AND

Z

0

0

0

1

1

0

1

1

NAND Truth table

3

The NOR logic gate

The NOR gate is effectively an inverted OR gate. In other words, the results obtained from the output are the opposite to that of the OR gate. This gate is often referred to as ‘NOT OR’. As with the NAND gate, when drawing up the truth table for the NOR gate it can be difficult to ‘picture’ or imagine the results. The best way to do this is to pretend that it is an OR gate and then invert (reverse) the results, thus giving you the outputs for the NOR gate.

A Z

B

SYMBOL FOR NOR GATE Task 2 Using the E&L boards once more, build up this circuit to confirm how a NOR gate works, and complete the truth table.

Switc h Unit

Power Connec tion

Switc h Unit

Nor Gate

Transduc er

Bulb

d rive r

Unit

A

B

OR

Z

0

0

0

1

1

0

1The X1OR logic gate

NOR Truth table

4

The XOR Logic Gate

This IC sends out logic when only 1 OR the other is sending logic 1. It will not work if both signals are sending out logic 1 like a normal OR gate does. This is why a XOR gate is sometimes known as an ‘X-Treme OR’ or an ‘Exclusive OR’

Z

Symbol for XOR Gate

Task 3 Using Crocodile Technology, build up this circuit to confirm how a XOR gate works, and complete the truth table.

A

B

OR

Z

0

0

0

1

1

0

1

1

XOR Gate

XOR Truth table

http://goo.gl/4uQfaP

5

Task 4 For each of the following examples, state whether the output Z is at logic 0 or logic 1.

(a)

1 Z

1

(b)

1 Z

0

(c)

1

Z

(d) 1 Z 1

(e) 1 Z 0

(g) 1 1

(f) 1 Z 1

Z

(h) 1

0

Z 6

Boolean Expressions

Each logic gate has a corresponding Boolean mathematical formula or expression. The use of these expressions saves us having to draw symbol diagrams over and over again.

NOT

A

Z

AND

A B

Z

OR

A

B

Z

NAND

A B

Z

NOR

A B

Z

XOR

A A B

Z

7

Combinational Boolean

So far, we have only looked at simple logic systems. In reality, most logic systems use a combination of different types of logic gates. This is known as ‘Combinational Logic’. Boolean Expressions can be worked out from these to know the equation for the circuit..

Example

A

B

Z

C

To work this out you have to take it one step at a time and work out the equation as it goes through each logic gate.

1. A A

B

Z

C

You can find out that the line for A soon turns into A

2. A

B C

A

A+B

Z

The lines for A and B now changes at it goes through the next logic gate.

3. A

B C

A

A+B

Z (A+B) .C

As we progress through the circuit we can now add C.

Z = . (A+B) C

8

Task 5 Work out the Boolean Expression for each of the following a)

A Z

B

b) A

B Z

C

c)

A B

C D

d) A

B

C

Z Z

9

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