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8. Digital
Technology
Chapter 8.1 – Analogue and digital
signals
Binary numbers
• In ordinary arithmetic, we use the decimal system to
represent number. Digits from 0 to 9 are used in this
system.
•In the binary system numbers are represented using only
two digits: 0 and 1.
Consider the decimal number 5037.
Digits: thousands
hundreds
tens
units
In fact, we could write this number in terms of powers of 10.
5037 = 5x103 + 0x102 + 3x101 + 7x100
Binary numbers
• So, the digits of a decimal number are just the
coefficients of various powers of 10. These
coefficients can be digits from 0 to 9.
• The same idea applies to binary numbers. But instead of
using powers of ten we will be using powers of 2. And the
coefficients be the digits 0 or 1 instead the digits from 0 to 9.
• To express a decimal number in the binary system, we must
write that number as a sum of powers of two with coefficients
that are either 0 or 1.
Example:
5 = 1 x 22 + 0 x 21 + 1 x 20
So, the binary representation of 5 will be
52 = 101
(or 0101 if we want to represent
it with four bits)
Binary numbers
Binary
12 = 1 x 23 + 1 x 22 + 0 x 21 + 0 x 20
122 = 1100
23
13 = 1 x + 1 x
132 = 1101
22
+0x
21
+1x
20
14 = 1 x 23 + 1 x 22 + 1 x 21 + 0 x 20
142 = 1110
…
Decimal
0
0
1
1
10
2
11
3
100
4
101
5
110
6
111
7
1000
8
1001
9
1010
10
1011
11
1100
12
1101
13
1110
14
1111
15
Binary numbers
• With four-bit words (that is, four digits) we can only
represent 16 number (from 0 to 15).
• For each of the four digits we have two choices: 0 or
1.
• The total number of choices is then 2 x 2 x 2 x 2 = 16.
• To represent larger number we have to increase the
number of bits in the binary representation of the
number.
Example:
43 = 1 x 25 + 0 x 24 + 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20
432 = 101011
Binary numbers
A simple way of converting a decimal number
into a binary number.
210 = 1024
29 = 512
753 = 512 + 128 + 64 + 32 + 16 + 1
28 = 256
27 = 128
26 =
64
25 =
32
24 =
16
23 =
8
22 =
4
21 =
2
20 =
1
So,
7532 = 1011110001
Binary numbers
• Given a number in binary form, we call the first nonzero digit the most significant bit (MSB) and the
last digit (the digit the number ends with) the least
significant bit (LSB).
For example, 01110 has 1 as it MSB and 0 as it LSB
• The MSB is associated with the highest power of 2,
and so it is the digit that mostly determines the value
of the number.
How microphones work
1.
2.
3.
4.
Sound waves carry energy toward the microphone.
The diaphragm moves back and forth when sound waves hit it.
The coil, attached to the diaphragm, moves back and forth as well.
The permanent magnet produces a magnetic field that cuts through
the coil. As the coil moves back and forth through the magnetic field,
an electric current flows through it.
5. The electric current flows out from the microphone to an amplifier or
sound recording device.
Analogue and digital signals
• When one speaks into a microphone, a voltage is
created in the microphone.
• The voltage is proportional to the actual physical
movement of the diaphragm of the microphone.
• A large voltage is created when the diaphragm moves
fast, and a small voltage when it moves slowly.
• The voltage signal so generated varies continuously
between two extreme values.
• Such signals are called analogue signals.
Analogue and digital signals
Analogue signals are continuous signals, varying
between two extreme values in a way that is
proportional to the physical mechanism that created
the signal.
Analogue and digital signals
A digital signals is a coded form of a signal that
takes the discrete values of 0 and 1.
Analogue and digital signals
•Consider a potential
divider circuit.
•The emf of the battery is 8V which means that the
reading of the voltmeter can be any number between 0
and 8, depending on where the lead connects to the
variable resistor R.
•The signal generated in the voltmeter is an analogue
signal.
Analogue and digital signals
• Imagine that the point of contact is moved from the
bottom end of the resistor to the top at constant
speed and assume that this is done in 4 ms.
• Then, the reading of the voltmeter would be the
time-dependant signal.
Analogue and digital signals
• This analogue signal must be sampled, which means it
must be measured.
• This is done at regular intervals of time.
• The number of times per second the signal is sampled is
called the sampling rate or sampling frequency.
• Sampling the signal means that we observe it for very
short intervals of time, wait, and then sample it again.
• Thus wee do not, in general, know hoe the signal
behaves in between the instants of time when it is
sampled.
• Typically, for audio signals, a sampling rate of 8000 times
per second is used.
• This means that such an audio signal is sampled every
1/8000=125 s.
Analogue and digital signals
• The actual duration of one sample is very short (1.0 s
or even less).
• This is why sampled signals are represented by
vertical lines of practically zero width.
• When a analogue signal is converted into a digital
signal, that is, when we convert a voltage into binary
number, we must decide how big will our bit word be.
• If we use two-bit words, the we will have at most 22 = 4
words (00, 01, 10, 11).
• If, instead, we use three-bit words, than we will have
23 = 8 words (000, 001, 010, 011, 100, 101, 110, 111).
Analogue and digital signals
• The range of the original voltage is divided into 4 levels
(if we use 2-bit words) and each level will be assigned
a 2-bit word.
• In each level there is a lower boundary and an upper
boundary
• In this case, there was a loss of information during the
digitization of the original data.
• To improve that, we must use a higher sampling frequency and
use 3-bit words or more.
Analogue and digital signals
• The process of dividing the range of the analogue signal
into a set of levels is called quantization and the levels
themselves are called quantization levels.
• The number of quantization levels is determined by the
length of the word to be used, that is, by the number of
bits used. With n bits the number of quantization levels is
2n .
• This gives rise to the notion of quantization error.
Suppose that the analogue signal varies from a minimum
value of m and a maximum value of M and we use n-bit
words to digitize it.
• The number of quantization levels is 2n, and so at each
sampling the analogue signal will take one of the 2n
values.
Analogue and digital signals
• The quantity
M m
q
n
2
is known as the quantization error of the digitization
process.
• Two analogue signals that differ less than the quantization
error are assigned the same binary number.
• Obviously, the bigger the quantization error, less accurate
the digital signal will be.
Analogue and digital signals
Compact disks
•A compact disk (CD) is a device on which information
can be stored in digital form and the retrieved.
• The CD is a disk of diameter 12cm. The analogue signal
is converted into a digital signal (‘0’s and ‘1’s) and then
imprinted on the CD.
•This is done by doing marks
called pits on the CD. The parts
of the CD without pits are called
lands.
•The edge of a pit corresponds
to binary ‘1’.
•A series of pits is made along a
path that spirals from the centre
of the disk outwards.
Compact disks
pit
1600 nm
land
500 nm
830 - 3560 nm
The path has a depth of 125nm.
Compact disks
• The bottom part of the disk (the side that is actually
being reads) is covered with optically transparent
material (polycarbonate).
•A CD is read using a laser beam.
The laser cannot have zero width.
•So when the beam is incident
near the edge of a pit, a few rays
will be reflected off the pit and the
rest will be reflected of the land.
•This causes destructive
interference and no light reaches
the sensor and this corresponds to
binary ‘1’.
Compact disks
Compact disks
Lands and pits and binary numbers
Compact disks
• The wavelength of the laser light used is about 780nm in
air.
• The refractive index of the polycarbonate material is 1.55,
which means that the wavelength of light in the
polycarbonate is:
air
780


 503nm
n 1.55
•The pit depth for destructive interference to occur must be:
 503
d 
 126nm
4
4
Compact disks
• The laser source moves outwards and so follows the
spiral of the pits and lands as the disk rotates.
• Because the circumference is getting longer as we
move outwards, the rate of rotation of the disk is
reduced, so that the laser can sample the disk at the
same rate.
• There are clearly many technical problems to be
solved here, such as stability, focusing on the right
part of the spiral, and timing.
DVDs
•The digital versatile
disk (DVD) is similar
to the CD in many
ways.
• Because the pit length is shorter than on a CD, more data
can be stored along the spiral.
• Also, data can be stored on both sides of the disk or in a
double layer on the same side.
• Overall, this results in more than seven times the storage
capacity compared to that of a CD.
Blu-Ray
Blue laser formats have a
shorter wavelength (405 nm)
then CD and DVD formats
which use a red laser (650
nm - DVD read wavelength).
Blue ray’s blue laser beam
focuses much tighter then a
red laser. This allows for
much tighter alignment of
pits (areas of darker contrast
on a recordable disc). This
tighter collection of pits
allows for greater storage,
27GB with the first
generation of single sided
blu-ray media.
LPs
• In Edison’s original sound recording in 1877, sound was
incident on a diaphragm, which therefore began to vibrate.
• A needle attached to the diaphragm then made marks on a
rotating tinfoil-covered cylinder.
• The ‘marks’ were a direct, mechanical copy of the actual
audio signal.
• During playback, the needle retraces the pattern scratched
on the cylinder surface and now makes the diaphragm
move, thus reproducing the sound stored.
LPs
• In the later vinyl LPs (Long-Play) the principle of
recording is essentially the same.
• But instead of a rotating cylinder, a flat rotating disk is
used.
• During playback the signal is amplified electrically and fed
into a loudspeaker, rather than making a diaphragm
vibrate.
• LPs have a very limited storage capacity and are subject
to damage by scratches and dust.
Cassettes
• These devices use magnetic
recording to store data in an
analogue form.
• They are called sequential devices
as you must wind the cassette to get
to the wanted song and this takes
some time.
• The recording takes place on the
ribbon of the cassette, which is made
out of a strong plastic coated in ferric
oxide, a ferromagnetic material.
• Ferric oxide can be permanently
magnetized when exposed to a
magnetic field.
Cassettes
•An analogue audio signal of music can be converted
to a varying electric current.
• This current produces its own varying magnetic field.
• When the cassette is exposed to this magnetic field, a ‘copy’
of this magnetic field is created on the tape.
• During playback, the magnetic field stored on the magnetic
tape will induce an electric current in a coil, which can be
converted into an audio signal playing the music that was
recorded.
• The advantages have been its low price and availability. Also,
the tape could be erased and new material recorded
• The disadvantages refer to the sequential nature of the
device, its limited storage capacity and being sensitive to high
temperatures and easily damaged.
Floppy disks
• The floppy disk, like the cassette, uses
magnetic recording.
• The original was invented in the mid-1960s
at IBM as a way of inputting data into a
computer as well as storing computer data.
• Its name comes from the flexible nature of
the disk.
• Data was stored magnetically but in
concentric rings, which had the advantage
that one could access data on an outer ring
without having to go sequentially through
the intermediate data as on a cassette.
• This provided a direct access storage
device.
Floppy disks
Floppy disks
Floppy Disk Drives
• Qume D/T 8, 8 inch drive, 1.2 MB. This drive was made in
1980.
• Tandon TM 100-2A with IBM logo, 5 ¼ inch drive, 360 KB.
This drive was made in 1983.
• Sony MPF920, 3 ½ inch drive, 1.44 MB. This drive was made
in 2004.
Hard disks
• Hard disks started being used only in computers.
• Nowadays, they are used in digital cameras, digital video
recorders, mobile phones and other devices.
• They store data in large quantities.
• The device itself consists of a number of disks made of
aluminium or glass arranged on a spindle.
• The surface of the disks is covered with a material that can
me magnetized (usually cobalt).
Hard disks
• The surface may be thought to be
divided into a very large number of
tiny regions and each such region
is the seat of a ‘0’ or a ‘1’ of
digitized data.
• The growth of hard disk capacity
has been exponential. Early PCs
had hard disks with a capacity of
just a few MB. Today’s PCs have a
hard disk capacity of hundreds of
GB.
• The data is stored in sectors and
tracks. Tracks are concentric rings
and a sector is a part of the same
track.
• The data can be accessed almost
instantly irrespective of its position
on the disk.
Advantages of digital storage
• The capacity for data storage is huge in digital
devices.
• The access to particular stored data is fast.
• The retrieval of data is fast.
• The storage is reliable.
• The stored data can be copied or erased easily.
• The stored data can be encrypted.
• The data can be processed and manipulated by a
computer.
• The data can be transported easily physically as
well as electronically.
Disadvantages of digital storage
• On the negative side, whereas an analogue
storage system, such as ordinary photographic
film, degrades slowly with time, a serious error with
a digital storage device is usually catastrophic, in
the sense that the data may never be recoverable.