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LANG

104

The audios of each unit’s content are available at www.anayaeducacion.es

is used to collect gy do you think What kind of technolo

Reading and listenin

You can see

Writing We write a variety of different styles and types of text relating to the unit topic, sometimes relating them to the UN Sustainable Development Goals. By practising different styles of writing, we improve our writing skills we need.

CONTENT DEVELOPMENT Highly structured content with important concepts highlighted in bold.

2 BASIC LOGIC GATES NAND gate Truth table A

Symbol

F 1

NOR gate Truth table A

Symbol

ã 2.4 The negation gates NAND and NOR A negative function can be understood as the result of applying the complement, or negation, operation to any of the AND and OR gates. But from an industrial point of view the NAND and NOR gates are enormously important. This is because less transistors are needed to manufacture NAND and NOR gates than to manufacture AND and OR gates.

Look at the table below, which shows the SI or Scale of Integration: Terminal 7 Terminal 14

A NAND gate has a complementary truth table to the AND gate. This means that, as long as any of the input variables have a value of 0, the output variable will take the value of 1.

Questions bag

2 Using logic gates with two inputs, draw the circuit outlines that correspond to the following logic functions: F=A+B+C

LOGIC CIRCUIT SIMULATION WITH LOGISIM

H = (A · B) + (A · C) M = (A · B) + (Ā · B) K = (A + B) · (Ā + B)

Meaning

Year

small

2-25

1960

medium

25-100

1965

giga large

10 -10

Unit 4

ã 4.1 Designing circuits

As you will see later on in the unit, logic gates are included in integrated circuits in a variety of ways. You may have to buy an integrated circuit in order to use just a single gate from the 6 or 8 gates usually available in each one. This waste can be avoided if you use an integrated circuit with NAND or NOR gates and you make use of any of its unused gates.

Utilities shortcuts

3,100,000 transistors

275,000 transistors

2,300 transistors

382,000,000 transistors

1,000,000,000 transistors

But how can we do this? Digital circuits included in microprocessors are reaching increasingly higher scales of integration. However, logic gate circuits have been Work canvas manufactured for the past three decades using similar technologies Components and with similar scales of integration. navigation pane

Logic gates are enclosed within integrated circuits and each one usually contains several gates that are supplied by a common active signal,Component usually referred to as Vcc. They have a common mass terminal properties and referred to aspanel GND, where a reference voltage value of 0 is connected. attributes

F = [Ā · B̄ · C̄] + [Ā · B̄ · C ] + [Ā · B · C̄] + [Ā · B · C ]

All chips or integrated circuits are manufactured following standardised models. The model shown in the picture at the top of this page, is

A prototype of an integrated circuit made by a dual in-line package 14-pin integrated circuit. Any logic gate or Jack Kilby. This American electrical engineer Thelogic first row hasconfiguration Utilities shortcuts options these are circuit usingunder this the format will menu, look similar. Other and physicist managed to integrate both passive useful and you will probably Look at are the table below. and active electronic components into one piece configurations that can use be them foundthe onmost. the market the SIL (single of silicon. It measured just 1.5cm and was the in-line package) circuits or integrated circuits placed directly onto the first integrated he was Access button circuit. In the year 2000 Utility button Utility device). The latter surface of the Access boards called SMD (surface-mount awarded the Nobel Prize for Physics. The hand allows you to change the digital values the Terminal industry. output pin. Normally, the functions are veryatcommon in the electronics circuit inputs. only have one output pin, which is the dependent variable of the function. However, in some cases you may want to monitor an 111 intermediate wire.

function, writing down all the possible combinations for the independent variables, and obtain the value of the corresponding function in each case.

110

A 114

Guided practice Let’s build a circuit, step by step, which implements this function: F = (A + B) · C

1996

1993 1985 1971 2010 2017 64 bit 32 bit 4 bit 64 bit 64 bit microprocessor microprocessor microprocessor Options menu microprocessor microprocessor

Obtaining NOT gates with NAND or NOR gates

3 Prepare a truth table for each

The icons included with some activities indicate the keys to the project.

Transistors used

S M

Look at the truth table of the NAND and NOR gates to verify this.

Z = (A · B · C) + Ā · C̄

Scale

Simulation programs help us save time when designing digital circuits. L large 100-1 000 1971 There are many simulation programs, but a good option for getting 5 started is Logisim. It is freeware that you can download if you 1982 search VL very large 1 000-10 for the following keywords in your search engine: cburch.com Logisim 6 1988can ultra large and simple 105-10to download. UL Logisim is very intuitive use, and you install it on Linux, Mac OS or Windows systems. 6 9 When you have installed it you will see the following window with XL the most extremely largeof which >10 different areas, important are9 shown in the2005 image below.

Reconverting a NOR gate or a NAND gate to get a NOT gate is very simple. You just need to connect the terminals of the input variables. This way, you allow only two possible inputs at the gate: a 0 or a 1, which are introduced the same way in all of the gate's inputs simultaneously.

G=A·B·C

Terminal 1

The digital symbol used to represent the function in a circuit diagram is based on the shape of the AND gate with a bubble that shows the negation of the original function. On the other hand, the NOR function represents the negation of the OR gate. A value of 1 is obtained as a result only in those cases where the input variables are 0 at the same time.

Understand, think, investigate...

In 1959, engineer Jack Kilby managed to integrate various semiconductor components onto the same substrate or base. He managed to enclose a whole circuit in a single component. From this point onwards, the majority of manufacturers started the race to integrate increasingly dense and complex circuits into a single chip. The complexity and density of an integrated circuit depends on the number of transistors in it. This is measured on the scale of integration. Since the early 1960s, the capacity to include a greater number of transistors in smaller pieces of semiconductor material has multiplied.

Terminal point 1 Front notch

The use of fewer transistors to manufacture a gate means lower energy consumption and a significant increase in the response speed of the gates. For this reason, hardware developers and engineers often prefer building circuits using techniques which involve the negation gates NAND and NOR.

SDG. Reflection on and analysis of SDGs, such as gender equality, climate action, reducing inequalities, etc.

Wide variety of pictures grouped according to content to aid your understanding.

Unit 4

DIGITAL INTEGRATED CIRCUITS

Model example

Guided practices and Model examples to help you learn new processes.

We speak about the different issues relating to the unit and the UN Sustainable Development Goals.

Speaking

use y objects which Name three everyda inside one up and seen 5 Talk to a partner. ics. Have you opened about how digital electron What do you know you describe it? it? How would

DIGITAL ELECTRONICS A world of zeros

Speaking

The arrow allows us to select components, or connect wires between components, by clicking on the left mouse button and dragging it to the desired position. If you draw a square on the canvas, all the components that are inside it can be moved without losing connections with the other components outside of the selection.

Shortcut to place a NOT gate on the canvas.

Text editing tool for writing indications on the canvas.

Shortcut to place an AND gate on the canvas.

Terminal input pin. One of these symbols is to be inserted for each independent input of the circuit’s logic function.

Shortcut to place an OR gate on the canvas.

Step 1 Expand the Gates folder in the components navigation pane and select the AND gate by clicking on it. Move the mouse to the work canvas and you will see that the gate appears. You can place it wherever you like. Repeat this operation with the OR gate. Place the OR gate to the left of the AND gate as you will be connecting them. It includes three square input pins, which will be the values of the variables, and a round output pin, which is the state of the dependent variable or function result.

Step 2 Use the left mouse button in the work canvas to make the connections between the components. If you need to connect the terminal of a component to another wire, you can do so by releasing the mouse button when you reach the wire. If you pass over it without stopping, the wires intertwine but do not connect. The input pins might not be facing the right way for you to be able to connect the wires. To change their orientation, you need to select them and change the Facing property in the attribute pane. In the diagram here, the square pins are facing down. You should make sure that the circuit looks like this.

Step 3 If you want the circuit to be more compact or to make a simple selection of one of the gates in order to move it, use the arrow tool, as explained in the table on the previous page.

Go to anayaeducacion.es to see videos on how to build a logic circuit with Logisim and simulate circuits in TinkerCAD.

115

KEYS

PROJECT

SDG

SDG Commitment Discover the Sustainable Development Goals and be an active part of our commitment to make a more equal and liveable world.

Developing thinking Work on strategies for thinking: reflect on the content you are learning, generate ideas, organise them, debate them, explain them…

Cooperative learning Get involved in your learning and participate in the group’s learning; you will find that cooperating improves performance and harmony in the class.

Emotional education Get to know yourself; identify the situations that bring up complicated emotions and manage them with constructive, self-affirming experiences.

NEW SECTIONS

Activities with different cognitive levels to check learning.

to choose Remember . for your portfolio

this resources from

unit

Unit 4

ctise review and pra

Binary Logic 1 Write down in your notebook how many combinations can be encoded in natural binary in the following cases, using 5 bits - 8 bits - 10 bits 12 bits

9 Assemble the following circuit using Logisim. Write the truth table for the function at the output of each logic gate in your notebook.

the first addend A1 and A0 and the second addend B1 and B0. Remember that the mathematical sum of two two-bit numbers can now result in a three-bit number. Take the sum of 2 and 3 as an example, which as you know results in 5, coded in binary as 101. Therefore, you need three bits for the output signal. You can assign names to the output variables in the following order C, D, and U, which make up the resulting number.

Also write the largest number that can be encoded in each of the above cases.

Glossary

2 Arrange the following four-digit binary numbers in descending order: 0110 - 0001 - 1001- 1111 - 1100 - 0101- 1101 - 0111

8. MEASURING ELECTRICAL QUANTITIES multimeter

3 Convert the binary number 0100101 into a decimal number. The positive side of a diode formed by p-type crystal. 10 Make the truth table of the following logic circuit. Basic The logic gates side of a diode formed by n-type crystal. Use Logisim to find the most simplified circuit. negative

12. LEDS

A device which can be connected in a circuit to measure different electrical quantities, such as voltage, current and resistance.

anode cathode

9. ELECTRICAL ENERGY AND POWER joule

The unit used to measure the quantity of heat energy.

watt-hour

The amount of energy consumed, calculated by multiplying the power in watts by the number of hours that a device is in use.

10. ELECTRICAL MACHINES

Glossary We learn the relevant terms that are underlined in the units with a clear definition.

alternator

A machine which transforms motion or mechanical energy into electrical energy in the form of alternating current.

armature

The fixed, external part of the alternator which houses the conductor.

dynamo

A machine which transforms motion or mechanical energy into electrical energy in the form of direct current.

electric motor

A machine which transforms electrical energy into movement or mechanical energy.

rotor

The part of a generator with magnets that is mobile and turns or rotates.

stator

The fixed part of an alternator which creates the magnetic field and makes the rotor move.

11. THE EFFECTS OF ELECTRIC CURRENT electrolysis

The effect when electric current passes through a substance and causes a chemical reaction.

electrolyte

A liquid that lets electricity flow through it.

joule effect

When kinetic energy is transformed into heat.

photons

Particles of energy that carry light radiation.

Transformer station

High voltage lines

Agricultural use

F=A·B+A·C·D

have any control over important and can affect the output. Describe the most characteristics following function: of TTL andthat CMOS technologies. Values affect the state of a system when they are changed, such on +a C) G =as (Atyping + B) · (Ā keyboard, pressing a switch or turning a dial. Simulating circuits in Logisim 12 Use Logisim to solve a circuit consisting of a open-loop control system A system which only allows previously programmed tasks to be carried out. one-bit mathematical adder. Open Logisim and 8 Preparing for the task. There is a logical output The result that we want to get from the control system, define an endAproduct or input action. and B as variables and D and U as function called EXCLUSIVE OR, or XOR, whose output variables. Use combination analysis and reference signal This setsisthe through the process, such truth table theconditions, following: which remain the same all the way define the truth table as seen below. The result is as setting a temperature on a thermostat. mathematical, not logical, so 1 + 0 = 0 + 1 = 01 and Inputs Output 1 = 10, which is the binary coded decimal number A B F=A5B 2. Create a logic circuit with the least possible 0 0 0 number of gates. 7

input

Inputs

Output

R1 = 250 kX

amplification factor

The relationship between the collector current and the base current, where the collector is higher than the base.

NPN transistors

Transistors with two layers of N-doped elements around a layer of P-doped elements which amplifies the current entering the base.

Transformation centre

Domestic use

249

Unit 4

Data input

Dn-1 Dn

The simplest multiplexer is a 2/1 multiplexer. This device was developed in the 74157 integrated circuit that operates with four equal multiplexers. The 74157 integrated circuit uses a Strobe input common to all four multiplexers in addition to the Vcc and GND power pins. If this has a high value (1) it inhibits them, in other words, none of them work. The multiplexers can only be used when Strobe* is at a low level (0).

To look at another example, integrated circuit 74153 contains two 4/1 multiplexers. In this case, each of the multiplexers, 1 and 2, have an inhibitor input (Strobe1G and Strobe2G), which are activated at low level (0). Each one of them has four inputs: 1C3-1C2-1C1-1C0 for multiplexer 1, and 2C3-2C2-2C1-2C0 for multiplexer 2. These will connect to their respective outputs 1Y and 2Y according the combination of the inputs SelectB and SelectA. Look at the operation board of multiplexer 1 to help you understand how it works.

VCC 16

Search for a manufacturer online and look for information about CMOS 4511 integrated circuits or TTL 7447 integrated circuits. Try to understand the distribution of the terminal and its operation.

12 Draw a block diagram representing a 4/1 multiplexer. Label the data bits, the selection bits and output Y.

Strobe VCC 16 1G Strobe 15 B 2G 1C3 A 14

Select

Strobe 15

4A 14

4B 13

1C2

2C3 13

1C1

2C2 12

1C0

2C1 11

4Y 12

3A 11

GND

1 2

3B 10

3Y 9

GND

74157

Strobe

A strobe light is one which flashes on and off very quickly. They are used as a visual effect to accompany electronic or rock music at concerts. How do you think they work?

The while loop executes a series of instructions continuously while the expression is true. The designers of Processing advise us to use it carefully, as the code inside the loop will be executed until it finds an exit condition. This could cause the mouse and keyboard actions to be outdated and may even block the Processing environment.

3 4

11 The decoder BCD is a special kind of decoder with

The while loop

A B C ... N

Select digital inputs

A Select pin acts as a selection input. If Select = 0, inputs 1A, 2A, 3A, and 4A are connected respectively to outputs 1Y, 2Y, 3Y and 4Y. If Select = 1, inputs 1B, 2B, 3B, and 4B are connected to their respective outputs 1Y, 2Y, 3Y and 4Y.

Understand, think, investigate...

There are two loops in Processing: the while loop and the for loop.

Output Y

while (expression) { Instructions in the loop are executed while the expression in brackets is true. One of the instructions must change the loop control variable so that the control expression becomes false. }

2C0 10 2Y 9

74153

SelectBSelectA

Model example

Output 1Y

void setup(){ size(500,200); smooth(); background(150); // Medium grey background noStroke(); // Shapes without borders } // End setup() void draw(){ int i = 50; // Loop control variable // will be used to vary the X coordinate while(i<width-25){ ellipse(i,height/2,25,25); // We draw the // ellipses in the coordinates that mark i and // (height/2) this way they will be vertically // centred i=i+50; // We increase i to exit the loop } // End while } // End draw()

Multiplexer blocked and inhibited

0-0

1C0

0-1

1C1

1-0

1C2

1-1

1C3

Prepare the task Connect a 0 or a 1 signal in the data bits so that it complies with the following table: SelectB-SelectA

Output 1Y

0-0

Maths

C REATE

Find out how Processing can be used in mathematics and geometry. Research examples from the Processing Library and see what structures you already know.

Understand, think, investigate... 33 Type the code from the example,

3 And what if we change the condition to (i>1)?

34 Change the code in the while example so the height of the ellipses fit to the height of the window.

35 Search for an explanation of while using the keywords: processing org reference while

0 0

36 Change the example by inputting

1-1

VCC OUT

3 Out

C2 = 10 nF

e) What happened when you made these changes?

GND

125

Design a digital electronic safety circuit PROJECT PRESENTATION

line(30, i, 80-i, i); line(0, i, 80-i, i); line(0, 80+i, 80-i, i); line(0, 80+i, 80, i);

The output will be considered as a variable F with a low level (0) when there is no danger. When it is at a high level (1), it will indicate that the robot must be stopped immediately.

Making the truth table

STEP 2

You can see that in the truth table, while A has a value of 0, function F will be 0. When A has a value of 1, function F will not report any danger until all the sensors are at low level (0).

START

Have you ever thought about how Technology, Programming and Robotics can be useful in Science?

Switch on robot

In all other combinations, variable F will have a high level (1).

Read sensors B, C and D

B = 1 or C = 1 or D = 1

F=AD+AC+AB and can therefore be simplified to F = A · [D + (C + B)] This way, we can use two-input gates. This means we need to use a two-input AND gate and two two-input OR gates, as we can see in the logic circuit diagram on the left. Using Logisim, check that when you change the inputs, the combinations comply with the functions in the truth table.

We need to begin by defining the input variables. The first input variable (A) indicates the operation of the robot. This is a variable which at low level (0) indicates an absence of danger because the robot is not working, and when it is at high level (1) it indicates that the robot is working. The other three variables (B, C and D) contain binary information indicating the position of a person in the vicinity of the robot with a high level (1).

In this section we create a cross-curricular project that joins Technology, Programming and Robotics with other subjects.

By using Logisim, function F is minimised to the following expression:

Let’s build a logic system which can deal with this situation.

Create

Simplifying logic function F

Define the variables

37 Now create two new variations

STEP 3

A car-repair garage uses a robotic arm to carry out paintwork. Since the robotic arm is mobile, a safety system with three presence sensors is needed. The sensors are arranged in 'positions of risk ' close to the robot, so that it will stop immediately when the sensors detect human presence in these areas. This problem occurs in many other systems, and the same solution can be applied.

STEP 1

the following variations:

121

Unit 4

KSHOP TECHNOLOGY WOR

and explain what they do.

Trust in your skills and knowledge, develop creativity, adapt to changing situations and have a proactive and responsible attitude.

CTRL 5

What happens if we change the size of the window to 300 x 100?

0-1

Enterprising culture

TRIG GND 1

These workshops put the ideas you have learnt in the unit into practice. You will be making things, using different computer programmes and practising your new skills.

2 What happens if we change the while condition to (i<1000)?

1-0

needed to implement the logic function F = Ā í D + B̄ í D̄ + B · C · D + A í B̄ í C̄ using a multiplexer. Search online for information on different devices and choose which one you think would be best.

THR

analyse the draw() function and answer the following questions:

Input the example that appears there, explain each line and the function of the instructions.

13 Draw an outline of the components and connections

C1 = 1 nF

RESET DIS

Technology Workshop

Unit 1

ä 2.9 Control structures. Loops A loop is a structure that contains a series of instructions to be executed again and again under a certain condition.

MUX

References to any extra resources that can be found in your digital resources.

Expand your English vocabulary by learning new words, phrases and grammar structures which we use when talking about technology.

D1 D2 D3 D4

d) Make the following changes to the basic circuit of the 555 integrated circuit: Change the 1 μF electrolytic capacitor to a 10 μF capacitor. Add an LED lamp at the output (pin 3 of integrated circuit 555) and add a 330 Ω protection resistor. Adjust the oscilloscope so that the time per division is 500 ms. The result should be similar to the diagram below.

Go to anayaeducacion.es to practise what you have learnt with the Study: Mind Map, Test yourself and Learn by playing interactive activities

The power or force that makes something turn around a central point in an engine.

Focus on English

A multiplexer is a circuit made of logic gates equipped with various logic inputs called data inputs, but with only one output. In a way, a multiplexer acts like a switch that connects one of its inputs with the output. Selecting which input is connected to the output is carried out by additional selection inputs. Look at the set-up in the picture on the right.

4 7 6

A coil of metal that will return to its original shape after it has been pressed down.

248

5.2 Multiplexers

Many digital circuits depend on a clock signal for synchronised operation. Let's assemble a stable circuit that can carry out this function and simulate it in Tinkercad. You need: a small breadbaord, a power supply, a 555 integrated circuit, a 10 nF capacitor, a 1 nF electrolytic capacitor, a 100kΩ resistor and a 250 kΩ adjustable resistor.

R2 = 100 kX

13 Using thedown sameand strategy asthe in activity 12, use two A short, solid piece of at metal moves up and makes function and write down leastinside three aoftube themwhich in two-bit variables to build a two-bit addend. Call parts of an engine move. your notebook.

124

VCC = 5 V

2. CONTROL SYSTEM ELEMENTS Find practical applications of the EXCLUSIVE OR piston

16 Using the logic function from the previous activity, conduct an analysis to work out which assembly uses fewer integrated circuits: the direct solution with a combination of NOT, OR and AND gates or the indirect solution which only uses NOR gates.

3. TRANSISTORS

Distribution

Industrial use

15 Simplify the following logic expression:

Digital integrated circuits Variables in the environment, or unexpected events,11which a control system doeswith not logic gates of the Draw the circuit diagram

torque Step-up transformer

b) What happens if you change the power supply value to 9V? What range of power supply is allowed in a 555 circuit?

6. CONTROL AND ROBOTICS 6 Draw the appropriate connections for a NOR gate to work as a negation gate. Could a NOT gate be 1. CONTROL SYSTEMS built using AND gates? closed-loop control system A system which allows adaptation to conditions and to the environment.

spring Power plant

a) Change the oscilloscope settings so that you can see the waveform clearly. When you can see it clearly, adjust the variable resistor to see how the signal period changes.

Explain the difference between a mathematical operation and a logic operation.

Assemble two circuits using Logisim, one using NOT, AND and OR logic gates, and another using two-input NAND gates. Copy both circuits in your notebook.

Production

14 Build the truth table which corresponds to the following diagram and write down the expression of logic function F.

5 Write the truth table of the NAND and OR functions using three independent variables.

disturbances

We'll use an oscilloscope to view the signal that’s generated.

YES Stop

Paint

STEP 4

Components and wiring The circuit is easy to assemble, as you only need two integrated circuits, copper wire and a breadboard.

List of components:

➜ L1 633 nm red LED ➜ R1 330 Ω ± 5 % resistor. ➜ U1 7432 integrated circuit, two-input OR gate. gate ➜ U2 7408 integrated circuit, two-input AND

STEP 5

In this case, we will use TTL technology. For the power supply we can use any of the variable voltage sources that we have in the workshop, which we set to 5 volts. The output of the function F will be an LED lamp.

Simulation in Tinkercad Use Tinkercad to create and simulate the circuit in action before assembling the physical version in the workshop. It should look like the picture on the left. We can see the following connections in the diagram on the left: Red wires: VDC, black wire: GND, blue wire for inputs A, B, C and D, orange wire for the F output, and a green wire for connections between logic gates. You can simulate entering values of 0 and 1 by connecting the inputs with GND or VDC. See what happens if you enter the combination 1111, that is, with all inputs connected to VDC. This is illustrated in the diagram here with purple wires, to distinguish them from the other wires used so far. Now you can see how the LED lights up and the current being consumed by the circuit increases. Check how the current values on an ammeter change depending on where it is connected. Make a note in your notebook of the current values you get from the different input combinations. Write down any conclusions you come to.

122

123

Academic and professional

ICT

orientation

Assessment

Linguistic Plan

Learn how to obtain information, select it and apply it; to plan, manage and work on projects; to collaborate online in an ethical and safe manner.

Evaluate your personal skills, discover and awaken your calling, train yourself to make decisions and learn to choose between different options.

Discover different strategies to analyse what you have learnt and how you learnt it; train yourself to take responsibility or overcome difficulties.

Use your communication skills in the different types of text that you will see. Language is always present, communicate!

RESOURCE BANK www.anayaeducacion.es digital book resource bank

Register at www.anayaeducacion.es to access your resource bank or download your digital book. You just need an email address, the code from the inside cover this book and permission from your parent or legal guardian.

A digital version of your book to be used online or offline. It offers access to your digital resources which are grouped by type or linked to unit content.

A space with resources, techniques and activities, designed to strengthen your knowledge. More about the keys

Resources related to THE project keys SDG

SDG Commitment with short videos that will help you understand the targets for reaching the Sustainable Development Goals worked on in this project.

Linguistic Plan with infographics that will give you models to work with the four linguistic skills, using different text types (descriptive, narrative, explanatory, etc.). Cooperative learning Preparing for the task In small groups, of four or five members: 1 All the members of the team will review how the assigned task can be accomplished. 2 To do this, the steps can be shared out to each team member who then in turn will explain how each part of the process can be done to the others. The others listen and participate if they think they can contribute something.

Authorship / adaptation : Variant of the Educational Innovation Laboratory of the colegio Ártica - David and Roger Johnson.

Developing thinking with explanations on how to apply the different thinking techniques proposed in the project.

3 Once everyone is in agreement on how to do each part, you will all complete the tasks and, finally, verify, among everyone, that you have solved it correctly.

Cooperative learning which includes descriptions of the cooperative learning techniques proposed in the project. Thinking techniques

Emotional education with resources to help you overcome any worries that may arise in different situations at school (beginning the school year, taking a test, etc.).

Logic Wheel This thinking technique will help you to establish phases when analysing specific content that you have to study.

Identify What is it? What is it like? Are there different types?

By following a logical sequence (the logic wheel), and by asking yourself a series of questions in each phase, you can:

• Identify content by asking yourself: What is it? What is it like? Are there different types? • Compare the content by formulating questions such as: In what way is it similar to ...? In what way is it different from ...? • Establish cause-effect relationships by asking yourself questions such as: Why? What impact does it have ...? • Argue, assess and ask yourself questions such as: What conclusions can be drawn after the analysis? What can be assessed or scored about it? Doing a data dump of these questions into a graphic organiser will help you. Authorship: Hernández, P., and García, L. A.; adapted by Escamilla, A.

Compare

Argue, assess What can we conclude?

Logic wheel

3 Establish cause-effect relationships Why? What impact does it have ...?

In what way is it similar to ...? In what way is it different from ...?

ICT resources to help you use information and communication technology in a healthy, correct and safe way.

Academic and professional orientation with information on different professions linked to the subject content.

Assessment which includes resources for your portfolio, as well as rubrics and targets that will help with your self-assessment.

Resources

Subject key concepts Additional content Mind Maps to help you study Simulations Learn by playing Videos and tutorials Language bank

Resources classified

by unit

All the resources are classified by unit so that you can find them more easily.

course contents

COMMUNICATION

Page 8

1. Electronic radiation.................................................................... 2. The ionosphere and electromagnetic signals........... 3. Wave modulation and transmission................................. 4. Transmitting signals through fibre optics..................... 5. Wireless transmissions through antennas.................... 6. Satellite communication..........................................................

DIGITAL ELECTRONICS

Page 104

10 13 14 18 20 22

1. Binary logic: states and voltage levels........................... 106 2. Basic logic gates.......................................................................... 108 3. Digital integrated circuits....................................................... 111 4. Logic circuit simulation with Logisim............................. 114 5. Decoders and multiplexers.................................................... 120

Technology workshop. Tracking artificial satellites........... 26

electronic safety circuit....................................................................... 122

Review and practise....................................................... 28

RESIDENTIAL INSTALLATIONS

Page 30

1. Electrical installations............................................................... 2. Sanitary and drinking water installations..................... 3. Gas installations............................................................................ 4. Climate control systems.......................................................... 5. Communications.......................................................................... 6. Security and home automation systems....................... 7. Regulationsa................................................................................... 8. Bioclimatic architecture...........................................................

32 44 52 54 58 62 63 70

Technology workshop. Analysing electrical

Technology workshop. Design a digital

Review and practise........................................................................ 124

PROGRAMMING WITH PROCESSING

Page 126

1. What is Processing?................................................................... 128 2. Graphical representation......................................................... 130 3. Control structures........................................................................ 138 4. Guided practice............................................................................ 146 5. Functions.......................................................................................... 148 Technology workshop. Make a game with

Processing................................................................................................. 150

Review and practise........................................................................ 153

installations............................................................................................... 72

Review and practise....................................................... 73

ANALOGUE ELECTRONICS

Page 76

1. Introduction..................................................................................... 2. Passive electronic components...................................... 3. Active electronic components............................................. 4. Fritzing: an OpenSource tool for assembling circuits............................................................. 5. Simulating analogue circuits with Yenka......................

78 80 82 90 94

Technology workshop. Make an oscillator.

An LED with a timer.............................................................................. 100

Review and practise....................................................... 101

COMPUTER CONTROL: ARDUINO AND PROCESSING

Page 154

1. Control systems............................................................................ 156 2. Arduino.............................................................................................. 159 3. Sensors............................................................................................... 163 4. Actuators.......................................................................................... 168 5. Arduino and Processing.......................................................... 172 Technology workshop. Program and design

an innovative traffic light control system..................................... 176

Review and practise........................................................................ 180

HYDRAULICS AND PNEUMATICS

Page 182

1. Introduction..................................................................................... 184 2. Physical operation principles................................................ 186 3. The components of pneumatic and hydraulic systems............................................................... 192 4. Symbols............................................................................................. 203 5. Basic circuits................................................................................... 206 6. Using simulators........................................................................... 212 7. Application in industrial systems....................................... 214 Technology workshop. Build a hydraulic machine............. 216 Review and practise........................................................................ 217

TECHNOLOGY AND SOCIETY

Page 220

1. Technological development throughout history...................................................................... 222 2. Analysis: the evolution of technological objects................................................................................................ 234 3. Sustainable development....................................................... 240 Review and practise....................................................... 242

TECHNOLOGY PROJECT A CO2 detector to prevent the spread of COVID in the classroom

Page 243

DIGITAL ELECTRONICS Reading and listening

A world of zeros and ones Mastering electricity is one of the greatest achievements of our era. We have developed efficient ways to generate and transport electrical energy so we can use it to power our households and make our lives much easier than before. A big breakthrough came with the development of electronics and digital electronics in particular. This technology allows us to control electronic devices and miniaturisation means these devices are compact and sleek in design. Although the control methods are complex, the theory which digital systems are based on is simple. It is different to analogue electronic systems, which work with continuously variable signal, as it only takes two values: high and low. These values are represented by 1s and 0s in binary code. This binary code can then be used to codify instructions or information for the device. So how can digital electronics help us to develop a fairer world? Sustainable Development Goal 3 is dedicated to ensuring good health and wellbeing throughout an individual’s life. It focuses on analysing the causes of illnesses, accidents and death. Therefore the goal aims to reduce the incidence of health emergencies and threats to wellbeing, especially in developing countries. Digital electronics can be fundamental in helping with this goal as it can help us examine the huge amounts of data related to public health. This in turns means we can implement new, or improve existing, healthcare systems. 1 What big changes did digital electronics bring about in terms of our electrical devices? 2 How would you describe a digital electronic signal? 3 How would you define the word sleek, from the first paragraph, in your own words? Why do people like products with a compact and sleek design? Think of more adjectives to describe modern electronic devices. You can see a video which introduces digital electronics at anayaeducacion.es.

104

Speaking 5 Talk to a partner. Name three everyday objects which use digital electronics. Have you opened one up and seen inside it? How would you describe it? What do you know about how it works? 6

What kind of technology do you think is used to collect health data?

7 Think about the aims of SDG 3 and how future developments in electronics will help with this goal. Consider these three aspects of modern life. a) Healthcare and wellbeing b) Technology for everyday use c) Work and industry

Technology will take over from humans in some workplaces. I read about it! I hope nobody will be paying too much for healthcare in the next decade.

Writing 8 Your class has discussed the advantages and disadvantages of digital electronic developments and how they might affect our health and wellbeing in the future. Your teacher has asked you to write an essay explaining the pros and cons.

NK E BANK A B E G A ANGU LANGUAG L ANK ANK GE BANK B B E E G G A A U U GUA K LANG ANG N L A L AN GE BANK 105 ANK GE BANK B B E E G G A A U U G A LAN LANG LANGUA LANGU

1 BINARY LOGIC: STATES AND VOLTAGE LEVELS Analogue signal Amplitude (wave length)

Frequency in Mhz

Time

An area of electronics which has been developing and expanding very quickly in recent decades is digital electronics. This is mainly because of the massive use of computers and automated control systems, which are operated with microprocessors. But it’s the global development of information and communication technologies, powered by the Internet, which is probably the biggest reason for the rapid evolution of this field of electronics. A digital circuit basically handles digital signals. A digital signal, also known as a binary signal, is a voltage that can only take two values. It has a lower value which is usually 0 volts, and a higher value which, depending on the technology used in the circuits, may be between 5 and 24 volts.

Digital signal

ãã1.1 Digital technologies

Amplitude

1 0 0 1 0 1

1 0 1 0 0 1

Time

The way a digital circuit operates does not depend on the type of semiconductors used. Instead, its operation depends on mathematical behaviour, which you will learn later in this unit. Two different types of technology are used to build circuits for different needs:

➜➜TTL technology (Transistor Transistor Logic). This technology

Machine languages Computers and digital machines use language based on binary codes to represent data, transmit it, carry out operations with it, and establish communication between different components and devices. The reason for using two digits is because digital technology uses transistors as basic control elements, making them work in only two states (on-off, open-closed, current flow-no current flow).

originated in the development of circuits based on bipolar transistors. It is known for its very fast processor technology and moderate consumption of energy. The latest TTL integrated circuit families have considerably reduced their energy consumption. The voltage values they use are 0 volts at low values and 5 volts at high values. These circuits are fed with 5 volts, the same as the high value.

➜➜CMOS technology (Complementary Metal Oxide Semiconductor) uses MOS transistors or derivatives of field effect transistors as a core element. These transistors stand out from others because they use higher voltage values to transmit a high value while using very low currents. This makes CMOS technology notable for its low consumption. Thanks to this, it has been possible to develop laptops, tablets and mobile phones, which all work without having to be plugged into a mains socket.

ãã1.2 Binary logic The use of high and low voltage values indicated for each type of technology establish binary logic states. A binary logic state can take two values that correspond to each voltage value. Generally, a positive logic is used, in which 1 is assigned to the high voltage, and 0 to the low voltage. These mathematical values are the basic ‘units’ of information we need. Each of these possibilities is called a combination. So, if you can only use one digit, there are two possible combinations, 1 or 0. But if you use two digits you will have 22 combinations. In other words, four combinations which are 00, 01, 10 and 11.

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Unit 4

ãã1.3 The natural binary numbering system When you write a sequence of numbers in the decimal system, you know that the position of the digit is important in showing its value. The final digit on the right is the unit. Then, moving to the left, the digits signify tens, hundreds, thousands, etc. When you write numbers in sequence starting from 1, after the number 9 you start to include another digit on the left. The next number starts with 1 and the digit on the right will change from 9 to 0. Therefore, after 9 you write 10. The same applies when you want to write the numbers that come after 99, 999, etc.

Bit A one-digit binary number is called a bit. This word comes from the joining of the words binary and digit. Encoding the number 3 in binary requires two bits and encoding the number 6 requires three bits.

The natural binary numbering system is exactly the same. The difference is that you only have two digits, 0 and 1, to compose the binary numbers. For this reason, when we are listing ordered binary numbers, writing 0 first and then 1, the following number is the combination of both, 10. Similarly, after writing the number 11, the next possible combination of the digits would be 100. Notice how after 111 comes 1000, and 1111 is followed by 10000, etc. Look at the tables below which show the first 16 binary numbers. In the right-hand column, you can see their corresponding number in the decimal system. Binary number

Decimal number

Binary number

Decimal number

1000

1001

1010

1011

100

1100

101

1101

110

1110

111

1111

It is also important to understand how binary numbers are converted into decimal numbers. The position of each digit indicates a value. The first value on the right indicates whether the number is even or odd, respectively, depending on whether it ends in 0 or 1. This is mathematically indicated as a value of 2°. The second digit on the right indicates whether it is a multiple of 2, therefore having a value of 21. If the third digit is a multiple of 4, it will have a value of 22 and so on. Let's see how a binary number is converted into its corresponding decimal. For example, 1101, look at the formula below: 1101 = 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 8 + 4 + 0 + 1 = 13. See this for yourself in the table. 25

Understand, think, investigate... 1 Convert the following binary numbers into their corresponding decimal numbers. a) 100101 b) 101010

c) 11001100

Binary number

Equivalent decimal number

1101

–

d) 11010101 e) 11010101 f) 10101010101

107

2 BASIC LOGIC GATES

Like decimal numbers, binary numbers can also operate together. These operations are divided into two large groups: mathematical operations and logic functions. The first group is made up of the usual operations: sum, difference, multiplication and division, using the same rules as algebra. However, binary logic is most useful in logic functions, which complies with a series of laws called Boolean algebra. For this reason, logic functions are called Boolean logic. Boolean algebra basically uses three logical operations:

➜➜logical complement or negation ➜➜logical sum ➜➜logical product The use of one or more of these logical operations in the same expression is called logic function. This function uses independent input variables, which may take any of the possible combinations by using the logic states 0 and 1 to produce a dependent variable or output variable. Any of these operations can be implemented with electronic circuits and are known as logic gates. A logic gate has inputs, which it receives electrical signals from. It also emits a high or low electrical signal via its output. This is the result of the logical operation. Below, we are going to look at how Boolean algebra defines basic operations by means of logic gates.

ãã2.1 Logical complement or negation The logical complement, or negation operation, establishes an output variable whose value is the opposite of the input variable. If we define an input variable as A, the operation is represented by a bar over the letter representing the logic variable. This way, Ā is the negation of variable A, so the complement function is written as F = Ā. This operation is implemented in a logic gate, the NOT gate. This, as a result, provides the inverse of the state of the input variable. If A is 1, Ā will take the value of 0. If, on the contrary, A is assigned the value of 0, Ā will take the value of 1. These values can be represented with a value table, known as a truth table.

NOT function truth table A

0 1

1 0

When representing this function schematically, the symbol used is a triangle with a small circle. This small circle, or bubble, is situated on its front vertex, as shown in the picture below. A

The symbols that are used within this unit of your textbook are those which are used most often to represent logical devices. They are from the American symbol system known as the Graphic Symbols for Logic Diagrams, or MIL, which originated in the US Air Force. Go to anayaeducacion.es to see a presentation about logic gates.

108

Unit 4

ãã2.2 The logical sum

Logical sum

The logical sum function applies to more than one variable. It is defined as an operation that results in 1 when at least one of the variables is 1. This same operation is achieved by connecting two switches in parallel. An electric current, for example, will find a way to keep on circulating when either of the two switches is closed. This function is represented with the + symbol, just like in mathematics. You should keep in mind that a logical sum and a mathematical sum are completely different operations. It is expressed mathematically as F = A + B. This is sometimes written with the ˇ symbol instead of a +, so it would be F = A ˇ B.

Truth table A

OR gate

B Electrical analogy A

In the right margin, you can see the symbol of this operation by means of a logic gate called an OR gate and the truth table which defines the output function, F, in the different combinations of inputs A and B.

ãã2.3 The logical product

Logical product

The logical product function is unique as it is a gate that allows the values of the variables to intersect. This means that the function is 1 only in the event that all input variables are that same value of 1. This is like when we connect two switches in a series circuit. If we apply this to a logic function with two inputs, for example A and B, we get the truth table which you can see here on the right. This is the logical product gate, which is also known as the AND gate, represented by the equation F = A · B. We can see that the function takes value 0 for all combinations except the one in which A and B both take the value 1. This is also sometimes written with the ˆ symbol instead of a +, for example F = A ˆ B.

Truth table A

OR gate

B Electrical analogy A

Model example Compound functions Based on the three logic gates NOT, OR and AND, more complex functions can be put together. Look at this mathematical expression, for example: F = (A + B) · C This expression states that the logical product C will be applied to the result of the logical sum of A and B. If you carry out the operations for each of the possible combinations of the three variables A, B and C you will obtain the truth table shown on the right. The outline of the digital circuit will be:

A B

109

2 BASIC LOGIC GATES NAND gate Truth table A

Symbol

NOR gate Truth table A

Symbol

ãã2.4 The negation gates NAND and NOR A negative function can be understood as the result of applying the complement, or negation, operation to any of the AND and OR gates. But from an industrial point of view the NAND and NOR gates are enormously important. This is because less transistors are needed to manufacture NAND and NOR gates than to manufacture AND and OR gates. The use of fewer transistors to manufacture a gate means lower energy consumption and a significant increase in the response speed of the gates. For this reason, hardware developers and engineers often prefer building circuits using techniques which involve the negation gates NAND and NOR. A NAND gate has a complementary truth table to the AND gate. This means that, as long as any of the input variables have a value of 0, the output variable will take the value of 1. The digital symbol used to represent the function in a circuit diagram is based on the shape of the AND gate with a bubble that shows the negation of the original function. On the other hand, the NOR function represents the negation of the OR gate. A value of 1 is obtained as a result only in those cases where the input variables are 0 at the same time.

Model example Understand, think, investigate... Questions bag

2 Using logic gates with two inputs, draw the circuit outlines that correspond to the following logic functions:

F=A+B+C

G=A·B·C

H = (A · B) + (A · C)

M = (A · B) + (Ā · B)

K = (A + B) · (Ā + B)

Z = (A · B · C) + Ā · C̄

F = [Ā · B̄ · C̄] + [Ā · B̄ · C ] + [Ā · B · C̄] + [Ā · B · C ]

3 Prepare a truth table for each function, writing down all the possible combinations for the independent variables, and obtain the value of the corresponding function in each case.

110

Obtaining NOT gates with NAND or NOR gates As you will see later on in the unit, logic gates are included in integrated circuits in a variety of ways. You may have to buy an integrated circuit in order to use just a single gate from the 6 or 8 gates usually available in each one. This waste can be avoided if you use an integrated circuit with NAND or NOR gates and you make use of any of its unused gates. But how can we do this? Reconverting a NOR gate or a NAND gate to get a NOT gate is very simple. You just need to connect the terminals of the input variables. This way, you allow only two possible inputs at the gate: a 0 or a 1, which are introduced the same way in all of the gate's inputs simultaneously. Look at the truth table of the NAND and NOR gates to verify this.

3 DIGITAL INTEGRATED CIRCUITS

Unit 4

A prototype of an integrated circuit made by Jack Kilby. This American electrical engineer and physicist managed to integrate both passive and active electronic components into one piece of silicon. It measured just 1.5cm and was the first integrated circuit. In the year 2000 he was awarded the Nobel Prize for Physics.

Scale

Meaning

Transistors used

Year

small

2-25

1960

medium

25-100

1965

large

100-1 000

1971

very large

1 000-105

1982

ultra large

105-106

1988

giga large

106-109

1996

extremely large

>109

2005

1993 1985 1971 2010 2017 64 bit 32 bit 4 bit 64 bit 64 bit microprocessor microprocessor microprocessor microprocessor microprocessor

3,100,000 transistors

275,000 transistors

2,300 transistors

382,000,000 transistors

1,000,000,000 transistors

Digital circuits included in microprocessors are reaching increasingly higher scales of integration. However, logic gate circuits have been manufactured for the past three decades using similar technologies and with similar scales of integration. Logic gates are enclosed within integrated circuits and each one usually contains several gates that are supplied by a common active signal, usually referred to as Vcc. They have a common mass terminal referred to as GND, where a reference voltage value of 0 is connected.

Fujitsu, an electronics factory in Malaga: an operator screwing pieces into a motherboard.

All chips or integrated circuits are manufactured following standardised models. The model shown in the picture at the top of this page, is a dual in-line package 14-pin integrated circuit. Any logic gate or logic circuit configuration using this format will look similar. Other configurations that can be found on the market are the SIL (single in-line package) circuits or integrated circuits placed directly onto the surface of the boards called SMD (surface-mount device). The latter are very common in the electronics industry. 111

3 DIGITAL INTEGRATED

Commercial format

CIRCUITS

Most logic gates are enclosed in plastic chips with terminals on both sides, known as dual in-line package, and normally have 14 pins. We can also find logic gates which are have 10, 12, 16 or 24 pins. You can do an online search to see what different digital circuit manufacturers have for sale.

Terminal point 1

Depending on the transistor technology used, integrated circuits will have different power consumption and electrical power characteristics. They also have different response and voltage levels for each logic state, although they all work the same way.

Front notch

TTL technology, which uses bipolar transistors, has a higher energy consumption rate but the response time at the output will be shorter. This technology is identified by the number 74, which is used as a prefix in the naming of integrated circuits.

Terminal 7 Terminal 14

Terminal 1

In addition, TTL technology is divided into several families that can be identified by one or two letters which follow the prefix 74: a 7404 integrated circuit, for example. In this integrated circuit model, six NOT gates are enclosed as standard, regardless of the manufacturer. Its low-power version is 74LS04 and its fast response version is 74H04.

NOT gate TTL integrated circuit series 7404 VCC

NAND gate TTL integrated circuit series 7400

NOR gate TTL integrated circuit series 7402

VCC

OR gate TTL integrated circuit series 7452

VCC

7 GND

On the other hand, CMOS (complementary metal oxide semiconductor) technology uses field effect transistors (MOSFET or MOS field-effect transistors). These transistors are different in that they are polarised by voltages instead of currents, as in the case of the bipolar transistors behind TTL technology. MOS transistors are smaller than bipolar transistors; they have significantly lower consumption and also allow CMOS circuits to regenerate impaired* signals. However, the signals evolve with much greater propagation delays. There are some technical solutions that can reduce propagation times though.

impaired: when something is damaged in such a way that it does not function as well as it should

112

Integrated circuits in this family are identified with a number that begins with a 4 (some examples include 4001, 4011, 4081) and they are the circuits which are the most frequently used today in microprocessor manufacturing, memory drives, digital signal processors and many other devices which require low power consumption. This is not only good for a compact design, it is also better in terms of sustainability and saving energy and money.

Unit 4

NOT CMOS 4069 series

NAND CMOS 4011 series

VCC

NOR CMOS 4001 series

VCC

OR CMOS 4071 series

VCC

7 GND

Understand, think, investigate...

I think, I’m interested, I investigate…

4 Find out what the following integrated circuits are:

d) What do we mean when we say that the value indicated in parameter IOH is negative?

CMOS

TTL

4071

7408

6 One of the logic gate parameters is known as fan-

4000

7410

4002

7421

out. Search for information on what it means and in which units it is measured.

4098

7430

7 Information from manufacturers’ catalogues below

4049

7408

e) In what temperature range can it operate?

shows the values of signal propagation through a gate. This indicates how long it takes to react when a change occurs at the input of a logic gate. Look at the data, which is measured in nanoseconds, and state the technology you think each one belongs to. Justify your answer.

5 The table below shows the data provided by a manufacturer in their product catalogue. They correspond to the integrated circuit of a two-input NAND logic gate. Look at the values and answer the following questions:

Logic family A

a) What is the power supply range of the integrated circuit?

Average

b) The second line shows the voltage that is admissible at HIGH level. Why is only the minimum value indicated? c) The VIL value also only has one piece of data, the maximum voltage value. Why is no other value indicated?

Propagation time

Logic family B

Maximum Average Maximum

100

Imagine that you have to transmit a signal through a thousand logic circuits. What will the maximum time difference be, depending on the technology you use?

Symbol

Parameter

Min

Nom

Max

Units

VCC

Supply Voltage

4.75

5.25

VIH

HIGH Level Input Voltage

VIL

LOW Level Input Voltage

0.8

IOH

HIGH Level Output Current

-0.4

IOL

LOW Level Output Current

Free Air Operating Temperature

ºC

113

4 Simulation programs help us save time when designing digital circuits. There are many simulation programs, but a good option for getting started is Logisim. It is freeware that you can download if you search for the following keywords in your search engine: cburch.com Logisim download. Logisim is very intuitive and simple to use, and you can install it on Linux, Mac OS or Windows systems.

LOGIC CIRCUIT SIMULATION WITH LOGISIM

When you have installed it you will see the following window with different areas, the most important of which are shown in the image below.

Options menu Utilities shortcuts

Work canvas Components navigation pane

Component properties and attributes panel

The first row has Utilities shortcuts under the options menu, these are useful and you will probably use them the most. Look at the table below. Access button

A 114

Utility

Access button

Utility

The hand allows you to change the digital values at the circuit inputs.

Terminal output pin. Normally, the functions only have one output pin, which is the dependent variable of the function. However, in some cases you may want to monitor an intermediate wire.

Shortcut to place a NOT gate on the canvas.

Text editing tool for writing indications on the canvas.

Shortcut to place an AND gate on the canvas.

Terminal input pin. One of these symbols is to be inserted for each independent input of the circuit’s logic function.

Shortcut to place an OR gate on the canvas.

Go to anayaeducacion.es to see videos on how to build a logic circuit with Logisim and simulate circuits in TinkerCAD.

Unit 4

ãã4.1 Designing circuits Guided practice Let’s build a circuit, step by step, which implements this function: F = (A + B) · C

Step 3 If you want the circuit to be more compact or to make a simple selection of one of the gates in order to move it, use the arrow tool, as explained in the table on the previous page.

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4 LOGIC CIRCUIT SIMULATION WITH LOGISIM

Guided practice Step 4

Selection: OR gate Facing

East

Data Bits

Gate size

Medium

Number of inputs

Output Value

0/1

Label

Label font

Sans Serif flat 12

Negate 1 (Above)

Label font

Go to the attribute pane and give the different pins and gates names by adding labels. All the components have a Label property where you can name them one by one. The input pins will be called A, B and C, the gates AND and OR, and the output pin F. In the case of the gates, you will have to modify other attributes according to the type of circuit. This might be the Number of inputs, which in this case will be restricted to 2, or the Gate size, which by default will appear as medium.

Understand, think, investigate... 8 Follow the same steps to build the functions below, using the information in brackets to help you make the connections:

F = (A + B) + (B · C)

G=A·B·C+Ā·B·C

H = (A · B) + (A · C̄)

9 Look at the circuit on the right and answer the following questions: a) What is the expression of F relative to the variables A, B and C? b) How many different gates does the circuit use? c) How many integrated circuits are needed to build the proposed logic function? d) Could you make changes in any of the components in order to use fewer integrated circuits?

116

Think and share with a partner e) Use the hand tool to change the input values. Mark all the combinations and state whether you notice anything strange in function F.

Unit 4

ãã4.2 Testing how the circuit works Often a logic circuit is designed for a specific need, such as solving a technical problem. The input variables, which are usually components such as environmental sensors or electrical mechanisms (e.g. switches or pushbuttons), are established first.

Inputs

Outputs

The output variables, which feed a specific actuator, are also identified beforehand. Finally, the truth table will show the mathematical relationship between them.

In these cases, Logisim will allow the variables and the truth table to be defined by using the option Window > Combinational analysis.

Let’s consider the truth table of a function with three input variables A, B and C, and an output variable F, whose values have been chosen at random.

We are going to work with the truth table that is in the top right corner of this page..

When you activate this part of the application, a window with several tabs pops up. In the first two on the left, Inputs and Outputs, you will have to name the variables. Type the variables A, B and C into the text box, one by one, pressing the Add button each time. Then, click on the Table tab and add the values of each combination in the spaces marked with an X. When you click on the X one time a 0 appears and with two clicks a 1 will appear. Once you have finished placing all the binary values into the F function, the simulator performs the calculation needed to obtain the mathematical expression. To do this, click on the Expression tab where you can check the simulation and the application of the Boolean algebra rule for simplifying expressions in digital functions. 117

4 LOGIC CIRCUIT SIMULATION WITH LOGISIM

You will notice that there are a total of four combinations in the truth table that result in 1. The function F will be obtained by adding up the four combinations. Each of the four addends corresponds to the product of the three variables A, B, and C so that the product of the three is 1. In the first combination ABC = 001, for function F to be 1, you have to write Ā · B̄ · C, so that by A having a value of 0, B a value of 0 and C a value of 1, we get Ā = Ō = 1, B̄ = Ō = 1 and C = 1. In total, the expressions affected in the F function are shown in the table below: Position of the addends in the truth table

Combination of ABC

Expression which results in: F = 1

2º

001

Ā · B̄ · C

3º

010

Ā · B · C̄

6º

101

A · B̄ · C

8º

111

A·B·C

F = Ā · B̄ · C + Ā · B · C̄ + A · B̄ · C + A · B · C The simplifying process followed by Logisim consists of trying to determine which part of the expressions does not affect the final result. Let’s make a concrete analysis of the second and sixth addends. Notice how both have expression B̄ C in common but the second addend has Ā and the sixth simply has A. In other words, what is important for the function to be 1 is that the expression B̄ C is maintained, while the value of A does not matter because it can be 0 or 1. This indicates that the expression of both addends can be reduced to the formula below: Ā · B̄ · C + A · B̄ · C = [Ā + A] · B̄ · C = [1] · B̄ · C = B̄ · C Once the expression of the second and sixth summands have been simplified, we have an even shorter formula: F = B̄ · C + Ā · B · C̄ + A · B · C Mathematical expressions which represent functions in Logisim If you click on the Minimised tab, a Karnaugh map is displayed in a square matrix below the selector, where all the 1s and 0s are shown. The second and sixth position appear adjacent to one another, shaded in pink. Logisim has found two simplifications on the map (the one shaded in pink and the one shaded in blue) and a combination, which because of its isolated situation, cannot be simplified: F = B̄ í C + Ā í B í C̄ + A í C When we look at the expression, we can see it is not the most simplified one in absolute terms. However, it is the most simplified expression in the sum of products format using the Karnaugh map. The first and third addends have the C variable in common, which could be simplified even further. But you will have to assess these subsequent simplifications because a simplification does not necessarily imply a cheaper solution. Finally, the only thing left to do is generate a digital circuit with logic gates by clicking Build Circuit. You will have to indicate the project you want to assign the circuit to if you have opened more than one. Then, give the circuit a name and select whether you want to use only two-input gates and if you only want to use NAND gates.

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Unit 4

ãã4.3 Looking for the cheapest way to build circuits

The method of simplification by using the Karnaugh map is a very effective way of simplifying functions without having to go into cumbersome* mathematical calculations. The expressions we get from this use the least number of gates.

cumbersome: when something is awkward because of size, weight, or shape. It also has the meaning of being difficult because of extent or complexity.

Logic gates, as you learnt in section 3 of this unit, are sold enclosed within integrated circuits. If you need different gates in the same solution, you may end up needing to buy three or four types of integrated circuits. In the process explained before, the last step of the Logisim program gave three options:

➜➜Creating the circuit with the gates which were proposed by the function's solution.

➜➜Creating the circuit by using gates equipped with only two inputs. ➜➜Creating a circuit using only NAND gates. This process is called the homogenisation of logic circuits. We will test all three options in order to assess which is the best solution and which uses the fewest integrated circuits. Check out these integrated circuits on the Internet in order to understand how many circuits are needed in each case. a) Circuit with heterogeneous gates using CMOS technology Logic gate

Number of gates

Integrated circuit

Number of integrated circuits

NOT

4 049

AND 2 Input

4 081

AND 2 Input

4 073

OR 3 Input

4 075

Total integrated circuits

b) Circuit with two-input heterogeneous gates using CMOS technology Logic gate

Number of gates

Integrated circuit

Number of integrated circuits

NOT

4 049

OR 2 Input

4 071

AND 2 Input

4 081

Total integrated circuits

c) Circuit with NAND homogeneous gates using CMOS technology Logic gate

Number of gates

Integrated circuit

Number of integrated circuits

NAND 2 Input

4 011

Total integrated circuits

For the function F, solutions b and c are the most appropriate. If we consider technical criteria related to accumulated delays in signal propagation in the circuit, we would choose b as the optimal solution. 119

5 In digital systems, integrated circuits with logic gates are not the only circuits. There are other types of circuits that carry out other functions, but that might also produce logic functions. These are called decoders and multiplexers.

DECODERS AND MULTIPLEXERS Inputs

ãã5.1 Decoders

Outputs

A decoder is a combinational digital circuit, which means it is made up of logic gates. Its operation depends on the number of inputs and outputs it has. So, we can find 2-input and 4-output decoders (called 2/4 decoders) and 3-input and 8-output decoders (called 3/8 decoders). Generally, they receive n inputs and produce 2n outputs. A decoder's operation is based on inserting natural binary code in its inputs, which activates a single output from all the possibilities available. Each output will indicate a combination of the input code. A 2/4 decoder has two binary inputs. Any of the four codes corresponding to each of the possible combinations can be entered into these: 00, 01, 10 and 11. Each of these input signals will trigger outputs D0, D1, D2 and D3 respectively. The most common 2/4 decoder in TTL technology is the one used in the integrated circuit 74VHC13. This decoder acts inversely, that is, its truth table considers negation signals as active signals. Look at the truth table and the arrangement of the terminals in the image on the right, taken from a manufacturer’s catalogue. Inputs

Outputs

Ē

Ō0

Ō1

Ō2

Ō3

− Ea

VCC

A0a

− Eb

A1a

A0b

— O0a

A1b

— O1a

— O0b

— O2a

— O1b

— O3a

— O2b

GND

— O3b

H = HIGH Voltage Level (1) L = LOW Voltage Level (0) X = Indifferent

Understand, think, investigate... 10 Go to the website of an integrated circuit manufacturer, like Fairchild, and try to find the 3/8 integrated circuit decoder. In your notebook, draw the arrangement of its terminals and write out its truth table.

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You will have noticed in the table above that H and L are used instead of 0 and 1, which indicate high or low voltage levels. It is essentially the same information because we will normally associate L = 0 and H = 1. However, in the distribution of terminals in the image on the left, you can see how the terminals are activated by L values, which often indicates activation through negation signals. This is why there is a bar on the name of each terminal. The 74VHC13 integrated circuit has two decoders, which can be used independently.

Unit 4

5.2 Multiplexers

D1 D2 D3 D4

Dn-1 Dn

VCC

Strobe

Strobe VCC 16 1G Strobe 15 B 2G 1C3 A 14

1C2

2C3

1C1

2C2

1C0

GND

Select

2 3

74157

Strobe 1

A strobe light is one which flashes on and off very quickly. They are used as a visual effect to accompany electronic or rock music at concerts. How do you think they work?

a 7-segment display. The BCD code is a particular type of binary code in which only the ten decimal numbers that can be represented by a single digit (0 to 9) are encoded using 4 bits. These decoders allow a decimal number encoded in binary as input, which then activates the outputs needed to light up a 7-segment display device. Search for a manufacturer online and look for information about CMOS 4511 integrated circuits or TTL 7447 integrated circuits. Try to understand the distribution of the terminal and its operation.

12 Draw a block diagram representing a 4/1 multiplexer. Label the data bits, the selection bits and output Y.

A B C ... N

Select digital inputs

11 The decoder BCD is a special kind of decoder with

Output Y

Data input

Understand, think, investigate...

MUX

2C1

2C0

74153

SelectBSelectA

Output 1Y

Multiplexer blocked and inhibited

0-0

1C0

0-1

1C1

1-0

1C2

1-1

1C3

Prepare the task Connect a 0 or a 1 signal in the data bits so that it complies with the following table: SelectB-SelectA

Output 1Y

0-0

0-1

1-0

1-1

13 Draw an outline of the components and connections needed to implement the logic function F = Ā í D + B̄ í D̄ + B · C · D + A í B̄ í C̄ using a multiplexer. Search online for information on different devices and choose which one you think would be best.

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ORKSHOP TECHNOLOGY W

Design a digital electronic safety circuit PROJECT PRESENTATION

STEP 1

Define the variables Let’s build a logic system which can deal with this situation. We need to begin by defining the input variables. The first input variable (A) indicates the operation of the robot. This is a variable which at low level (0) indicates an absence of danger because the robot is not working, and when it is at high level (1) it indicates that the robot is working. The other three variables (B, C and D) contain binary information indicating the position of a person in the vicinity of the robot with a high level (1).

Making the truth table

STEP 2

You can see that in the truth table, while A has a value of 0, function F will be 0. When A has a value of 1, function F will not report any danger until all the sensors are at low level (0).

START

Switch on robot

In all other combinations, variable F will have a high level (1).

Read sensors B, C and D

B = 1 or C = 1 or D = 1

YES Stop

122

The output will be considered as a variable F with a low level (0) when there is no danger. When it is at a high level (1), it will indicate that the robot must be stopped immediately.

Paint

Unit 4

STEP 3

Simplifying logic function F By using Logisim, function F is minimised to the following expression: F=AD+AC+AB and can therefore be simplified to F = A · [D + (C + B)] This way, we can use two-input gates. This means we need to use a two-input AND gate and two two-input OR gates, as we can see in the logic circuit diagram on the left. Using Logisim, check that when you change the inputs, the combinations comply with the functions in the truth table.

STEP 4 List of components:

➜➜L1 633 nm red LED ➜➜R1 330 Ω ± 5 % resistor. . ➜➜U1 7432 integrated circuit, two-input OR gate gate ➜➜U2 7408 integrated circuit, two-input AND

STEP 5

Components and wiring The circuit is easy to assemble, as you only need two integrated circuits, copper wire and a breadboard. In this case, we will use TTL technology. For the power supply we can use any of the variable voltage sources that we have in the workshop, which we set to 5 volts. The output of the function F will be an LED lamp.

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Binary Logic 1 Write down in your notebook how many combinations can be encoded in natural binary in the following cases, using 5 bits - 8 bits - 10 bits 12 bits

9 Assemble the following circuit using Logisim. Write the truth table for the function at the output of each logic gate in your notebook.

Also write the largest number that can be encoded in each of the above cases. 2 Arrange the following four-digit binary numbers in descending order:

0110 - 0001 - 1001- 1111 - 1100 - 0101- 1101 - 0111 3 Convert the binary number 0100101 into a decimal number.

Basic logic gates 4

10 Make the truth table of the following logic circuit. Use Logisim to find the most simplified circuit.

Explain the difference between a mathematical operation and a logic operation.

5 Write the truth table of the NAND and OR functions using three independent variables. 6 Draw the appropriate connections for a NOR gate to work as a negation gate. Could a NOT gate be built using AND gates?

Digital integrated circuits 7

Describe the most important characteristics of TTL and CMOS technologies.

Simulating circuits in Logisim 8

Preparing for the task. There is a logical function called EXCLUSIVE OR, or XOR, whose truth table is the following: Inputs

Output

F=A5B

Assemble two circuits using Logisim, one using NOT, AND and OR logic gates, and another using two-input NAND gates. Copy both circuits in your notebook. Find practical applications of the EXCLUSIVE OR function and write down at least three of them in your notebook. 124

11 Draw the circuit diagram with logic gates of the following function: G = (A + B) · (Ā + C) 12 Use Logisim to solve a circuit consisting of a one-bit mathematical adder. Open Logisim and define A and B as input variables and D and U as output variables. Use combination analysis and define the truth table as seen below. The result is mathematical, not logical, so 1 + 0 = 0 + 1 = 01 and 1 = 10, which is the binary coded decimal number 2. Create a logic circuit with the least possible number of gates. Inputs

Output

13 Using the same strategy as in activity 12, use two two-bit variables to build a two-bit addend. Call

Unit 4

We'll use an oscilloscope to view the signal that’s generated.

14 Build the truth table which corresponds to the following diagram and write down the expression of logic function F.

a) Change the oscilloscope settings so that you can see the waveform clearly. When you can see it clearly, adjust the variable resistor to see how the signal period changes. b) What happens if you change the power supply value to 9V? What range of power supply is allowed in a 555 circuit? 15 Simplify the following logic expression: F=A·B+A·C·D 16 Using the logic function from the previous activity, conduct an analysis to work out which assembly uses fewer integrated circuits: the direct solution with a combination of NOT, OR and AND gates or the indirect solution which only uses NOR gates. 17

c) Search for information about 555 integrated circuits. Draw the pin configuration in your notebook and write what each pin is for. Find out its operation modes and write the formulas that allow us to calculate the parameters of the wave based on the values of the components. d) Make the following changes to the basic circuit of the 555 integrated circuit: Change the 1 μF electrolytic capacitor to a 10 μF capacitor. Add an LED lamp at the output (pin 3 of integrated circuit 555) and add a 330 Ω protection resistor. Adjust the oscilloscope so that the time per division is 500 ms. The result should be similar to the diagram below.

VCC = 5 V R1 = 250 kX

R2 = 100 kX

C1 = 1 nF GND

RESET VCC 7 DIS 6 3 THR OUT Out 2 TRIG GND CTRL 1 5 C2 = 10 nF

e) What happened when you made these changes?

Go to anayaeducacion.es to practise what you have learnt with the Study: Mind Map, Test yourself and Learn by playing interactive activities

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