Digital technology

Topic 14.1: Analogue and digital signals

Digital technology

14.1 Analogue and digital signals 14.2 Data capture; digital imaging using

charge-coupled devices (CCDs)

Decimal numbers

The decimal number system (base 10) is the most widely used number system.

It uses ten different digits:

0,1,2,3,4,5,6,7,8 and 9

Binary numbers

The binary number system (base 2) is the most widely used number system in computers

It uses two different digits:

0 and 1 Each binary digit is called a ‘bit’. For example, the number 10010111 is 8 bits

long.

Least-significant bit (LSB)

In computing, the LSB is the bit position in binary number giving the units value.

In this 8 bit binary number the highlighted number is the LSB:

The LSB is sometimes called the right-most bit.

Most-significant bit (MSB)

In computing the MSB is the bit position in binary number having the greatest value.

In this 8 bit binary number the highlighted number is the MSB:

The MSB is sometimes called the left-most bit.

Converting binary numbers into decimal numbers

To convert a binary number into its decimal number the you start from the right hand number which represents a 1.

Each number afterwards represents double the number before.

Then add then numbers with 1s together!

Converting binary numbers into decimal numbers

What is 10111 in decimal form?

10111 = 164 + 4

2 + 2

1 + 1

0

= 23

Binary number 1 0 1 1 1

Place 16 8 4 2 1

Examples

Convert these binary numbers to decimals

11001 11010001 11110001 10011011

Converting decimal numbers into binary numbers

To convert a decimal number.

First write out the binary equivalents. (No more than five for IB)

16,8,4,2,1

Put a 1 if you are using the number to make the decimal one or a zero if not!

Examples

Convert these decimal numbers to binary:

9 15 19 28 23

ASCII Code• Converts letters to 0 and 1s for the

computer.

• Each letter is a 8 bit code (1 byte)

What are analogue signals? Analogue is a continuously varying signal

. Can be stored on LPs and audio tapes.

To be stored on CDs, DVDs etc… they must first be converted to digital.

The electrical signal between a microphone and a speaker is an analogue signal

Electrical signal of a conversation

At the other end

The electrical signal is then turned into sound by a speaker and you can hear the voice

The electrical signal is not perfect and there will be ‘noise’, often heard as a hiss

Analogue signal with medium signal to noise ratio

-4

-3

-2

-1

0

1

2

3

4

Problems

The electrical copy is not perfect The electrical wires have resistance and so

the voltage will decrease This limits how far the signal can be sent as

the signal will be too low compared to the noise

A solution?

It is difficult to distinguish between the analogue signal and the noise

A solution is to turn the conversation into a digital signal.

This is an analogue to digital conversion

What are digital signals?

Digital - A method of storing, processing and transmitting information through the use of distinct electronic or optical pulses that represent the binary digits 0 and 1.

Converting Analogue to Digital

PAM – Pulse amplitude modulated signal

Measure the amplitude of the signal at regular intervals. This is called sampling

-4

-3

-2

-1

0

1

2

3

4

1 Sec

Sampled at 2 Hz

Signal Consisting of 1 Hz, 5 Hz and 10Hz

Sampled at 5 Hz

Signal Consisting of 1 Hz, 5 Hz and 10Hz

-4

-3

-2

-1

0

1

2

3

4

1 Sec

Here we seem to obtain a good sin wave at a frequency which was not present in the original signal. This is called ‘Aliasing’.

-4

-3

-2

-1

0

1

2

3

4

1 Sec

Sampled at 10 Hz

Signal Consisting of 1 Hz, 5 Hz and 10Hz

-4

-3

-2

-1

0

1

2

3

4

1 Sec

Sampled at 20 Hz

Signal Consisting of 1 Hz, 5 Hz and 10Hz

-4

-3

-2

-1

0

1

2

3

4

1 Sec

Sampled at 40 Hz

Signal Consisting of 1 Hz, 5 Hz and 10Hz

Conclusion1. Complex signals are made up of many sine waves of

different Frequencies and Amplitudes.

2. If we wish to sample these signals in such a way as to be able to reconstitute the original signal, the sampling rate must be at least twice the maximum frequency present.

3. A sampling rate of twice the maximum frequency present is called the ‘Nyquist Rate’ (Each sampled signal has its own Nyquist Rate)

4. For satisfactory sampling:

1. If the sampling rate is too slow, ‘Aliasing’ can occur.

RateNyquistRateSampling

Why 40,000 Hz??

Sound is often sampled at 40,000Hz… Can you think why??

Storage of information

Storing Analogue signals

There are two main ways of storing analogue signals,

• either as variations in the surface of a plastic (vinyl) disc - a record, or

• variations in the arrangement of magnetic particles attached to a plastic tape - reel to reel tape or cassette tape.

For a record, a spiral groove is pressed into the surface of the vinyl disk.

The depth of the groove varies with the value of the analogue signal being stored.

To recover the analogue information from the disc, the disc is rotated at a constant angular speed and a stylus is placed into the groove.

As the disc rotates, the stylus moves along the groove picking up the variation in depth.

A magnet attached to the stylus moves in and out of a coil of wire with the depth variations, so turning this into an analogue electrical signal.

se c tio n o f a re c o rd

s ty lu s fle x ib le sh a ft

c o il o f w ire

m a g n e tw ire s c a rry in g

th e a n a lo g u e s ig n a l

se c tio n o f a re c o rd g ro o v e

p ic k -u p a rm

For a tape recorder, the analogue signal is stored on a very thin piece of plastic (mylar) coated in very fine particles of

magnetic iron or chromium oxide.

The tape passes at a constant speed in front of a tape head.

The analogue signal is applied to the coil in the tape head.

This causes a strong magnetic field to develop in the gap at

the front of the tape head, which is in contact with the tape.

The magnetic particles on the tape align with the magnetic

field in the gap, and maintain this alignment after the tape has

moved past the head.

ta p e h e a d

m a g n e tic ta p e

g a p

c o il a n a lo g u e s ig n a l

d ire c tio n o f tra v e l o f th e ta p e

m a g n e tic ta p e

Storing digital information

The most popular methods of storing digital information include Compact Discs (CDs and DVDs), Hard disks (as in Computer systems) and solid state flash memory (Memory sticks and cards).

A CD consists of polycarbonate plastic impressed with a single spiral track of data, 0.5 microns wide with 1.6 microns separating one data track from the next, circling from the inside of the disc to the outside. Once the plastic has formed it's coated with reflective aluminum and a clear acrylic layer to protect the aluminum.

The laser beam scans the spiral from the centre of the disk and is reflected from the tracks, either weakly due to scatter (logic 1) or strongly due to simple reflection (logic 0), and is detected by a photo-transistor.

The CD data is arranged in spiral tracks some 1.6m apart.

The pits are a minimum of 0.83µm long, 1.6µm apart and 125nm deep.

DVD pits are 0.4microns, 0.74 microns apart and 120nm deep.

The space between two holes is called an island.

A CD will hold around 700MB of data while a single sided standard DVD will hold around 4.7GB of information.

1 .6 m

5 0 0 n m

5 0 0 n m

is la n d s

C D

© ikes0 8 0 78 3 0 n m

7 4 0 n m

3 2 0 n m

3 2 0 n m

is la n d s

D V D

© ikes0 8 0 74 0 0 n m

Light that strikes the areas of the CD without pits is reflected normally.

Light that strikes a pit undergoes destructive interference with the light reflected from the area surrounding the pit.

This occurs because the depth of each pit is one quarter of the wavelength of the laser light.

Do you know why ¼ of wavelength?

The height of the pit is 1/4 of the wavelength of the laser light when travelling in polycarbonate, so that light reflected from the pit has a phase difference of one-half wavelength.

The light reflected from the bump and from the surrounding land cancel each other out.

The wavelength of the laser radiation

for a CD is 780nm,

for a DVD it is 650nm and

for the new high density DVDs it is 405nm.

Initially CDs were designed to operate by interference of the light.

The light reflected from a island had a path difference of /2 compared to light reflected from the surrounding area, resulting in destructive interference and so a reduction on the light intensity at the detection system.

This means that the height of each bump must be /4 of the wavelength of the light in the polycarbonate layer, i.e. 125nm.

Higher Storage Capacity

Same principle… much higher capacity

Laser – DVD laser has a wavelength of 640nm so it can read smaller pits

Track – Each pit is half the size of the pits on a CD making the track length twice as long

Layers – You can double the information having two layers of pits. Top layer is coated with a semi- reflective coating so light can pass through to the bottom layer.

A hard disk consists of several very flat disks coated with ultra fine coating of magnetic oxides. These disks rotate very fast, some as fast as 15000rpm.

The recording and replay system is similar to that of the magnetic tape, except that, because the disks are rotating so quickly, the read/write heads just skim the surface without touching the disk.

A major advantage of magnetic disk systems over magnetic tape is that the data can be accessed randomly, since the head can quickly move to any part of the rotating disk.

Solid state flash memory cards are essentially very complex integrated circuits containing billions of NAND (or NOR) gates arranged as bistable latches with each latch storing 1 bit of information.

As the manufacturing techniques of integrated circuits continues to develop, it is quite likely that these will eventually replace hard disk systems.

Analogue Digital

LPs, cassette tapes CDs, DVDs, hard discs

information is stored in continuous, variable form

information is stored in discrete form

LP: 22-26 minutes per side; 2 sides CD: approx 80mins

needle travels fastest on the outside edge

change their speed of rotation to provide constant linear velocity

Play from the outer radius inwards

Play from the inner radius outwards

Information storage

Advantages of storing information in a digital form are: Quality

Digital data has the major advantage that the quality does not deteriorate no matter how many times it is copied.

With analogue data, noise is added to the information each time it is copied, resulting in a degradation of the quality of the information.

ReproducibilityDigital data can be copied quickly and readily. Error checking and

correction ensure it does not become corrupt. It is not possible to apply error checking and correction techniques to analogue data.

Retrieval speedDigital data can be retrieved at high speed especially from Random

Access Memory devices, e.g. hard disk drives, CDs, DVDs, NAND gate memories, etc. Retrieval of data from tape systems is much slower and is comparable to the speed of access with analogue systems.

Portability

Manipulation of dataA further major advantage of Digital data is that it can be encrypted,

i.e. put into a form so that a special decoding 'key' is needed to be able to access the information. This prevents unauthorised reading of the information by anyone other than those with the encryption key. It is not possible to encrypt analogue data without seriously degrading the quality of the information.

Advantages and disadvantages Advantages of Digital:

Less expensive More reliable Easy to manipulate Flexible Compatibility with other digital systems Only digitised information can be transported through a noisy

channel without degradation Integrated networks

Disadvantages of Digital: Sampling Error Digital communications require greater bandwidth than analogue

to transmit the same information. The detection of digital signals requires the communications

system to be synchronised, whereas generally speaking this is not the case with analogue systems.

Advantages and disadvantages

Advantages of Analogue - Uses less bandwidth More accurate

Disadvantages of Analogue - The effects of random noise can make signal

loss and distortion impossible to recover

Issues for society of ever-increasing data storage

As it becomes possible to store more and more data there are implications for society:

Storage:- It is estimated that the world generated 161 billion gigabytes (161 exaBytes) of digital information in 2006. This will only increase year on year.

Cataloging all of the digital information available is a major problem. It is likely that there are many identical copies of the same information held on separate systems. Accessing the right information is a major issue and the scale of the problem again increases year on year.

Moral:- personal data stored and available very quickly e.g. police records, credit ratings, mobile phone records, internet records.

Ethical:- data bases 'talk' to each other - data can be matched so that a complete set of personal data can be easily obtained. The recent growth in closed circuit television cameras (CCTV) means that where ever you go in a large city you are likely to be captured on camera. These images are stored digitally and so can be used to monitor where you go.

Piracy:- Video and audio data can be copied flawlessly leading to a large market of illegal music and film discs. This deprives the copyright holders of the materials of important revenue which they are then not able to use to produce more music/films.

Data centres:- To store all of the online digital information requires large 'Data Centres' which are packed with racks of high performance computers (servers). These consume a significant amount of power both to operate and to keep cool. It is estimated that 2.5% of the green house gases produced by the UK is as a result of the operation of data centres.

Waste:- The life cycle of a computer is approximately four years. Even though the computer may still be working, advances in software and storage capacity result in it being necessary to upgrade to a new machine. The disposal of this redundant equipment poses a serious problem. As well as the disposal of the hardware there is also a major disposal problem associated with the general waste of resources, e.g. the polycarbonate thrown away in CDs each year.

Back up of data:- With such huge quantities of data produced each year, a major problem is the backing up of this data to ensure it is not lost by hardware failure, software or operator errors.

One click of a mouse button could completely destroy years of data!