1.

2 Text, sound and images

Example 4
The following 12-bit binary number represents denary number 1676:
−2048 1024 512 256 128 64 32 16 8 4 2 1

0 1 1 0 1 0 0 0 1 1 0 0

Applying two’s complement (1 0 0 1 0 1 1 1 0 0 1 1 + 1) would give:

−2048 1024 512 256 128 64 32 16 8 4 2 1

1 0 0 1 0 1 1 1 0 1 0 0

In other words: −1676

Activity 1.13
Convert the following negative denary numbers into binary numbers using the
two’s complement format:
a −18 c −47 e −88 g −100 i −16
b −31 d −63 f −92 h −1 j −127

Activity 1.14
Convert the following negative binary numbers (written in two’s complement
format) into negative denary numbers:

a 1 1 0 0 1 1 0 1

b 1 0 1 1 1 1 1 0

c 1 1 1 0 1 1 1 1

d 1 0 0 0 0 1 1 1

e 1 0 1 0 0 0 0 0

f 1 1 1 1 1 0 0 1

g 1 0 1 0 1 1 1 1

h 1 1 1 1 1 1 1 1

i 1 0 0 0 0 0 0 1

j 1 1 1 1 0 1 1 0

1.2 Text, sound and images

1.2.1 Character sets – ASCII code and Unicode
The ASCII code system (American Standard Code for Information Interchange)
was set up in 1963 for use in communication systems and computer systems.
A newer version of the code was published in 1986. The standard ASCII
code character set consists of 7-bit codes (0 to 127 in denary or 00 to 7F in
25

318281_C01_CAM_IGCSE CO_SCI_001_044.indd 25 18/02/21 3:22 PM

 1 Data representation

hexadecimal) that represent the letters, numbers and characters found on a

standard keyboard, together with 32 control codes (that use codes 0 to 31 (denary)
or 00 to 19 (hexadecimal)).
Table 1.2 shows part of the standard ASCII code table (only the control codes
have been removed).
▼ Table 1.2 Part of the ASCII code table

Dec Hex Char Dec Hex Char Dec Hex Char

32 20 <SPACE> 64 40 @ 96 60 `
33 21 ! 65 41 A 97 61 a
34 22 “ 66 42 B 98 62 b
35 23 # 67 43 C 99 63 c
36 24 $ 68 44 D 100 64 d
37 25 % 69 45 E 101 65 e
38 26 & 70 46 F 102 66 f
39 27 ‘ 71 47 G 103 67 g
40 28 ( 72 48 H 104 68 h
41 29 ) 73 49 I 105 69 i
42 2A * 74 4A J 106 6A j
43 2B + 75 4B K 107 6B k
44 2C , 76 4C L 108 6C l
45 2D - 77 4D M 109 6D m
46 2E . 78 4E N 110 6E n
47 2F / 79 4F O 111 6F o
48 30 0 80 50 P 112 70 p
49 31 1 81 51 Q 113 71 q
50 32 2 82 52 R 114 72 r
51 33 3 83 53 S 115 73 s
52 34 4 84 54 T 116 74 t
53 35 5 85 55 U 117 75 u
54 36 6 86 56 V 118 76 v
55 37 7 87 57 W 119 77 w
56 38 8 88 58 X 120 78 x
57 39 9 89 59 Y 121 79 y
58 3A : 90 5A Z 122 7A z
59 3B ; 91 5B [ 123 7B {
60 3C < 92 5C \ 124 7C |
61 3D = 93 5D ] 125 7D }
62 3E > 94 5E ^ 126 7E ~
63 3F ? 95 5F _ 127 7F <DELETE>

26

318281_C01_CAM_IGCSE CO_SCI_001_044.indd 26 18/02/21 3:22 PM

 1.2 Text, sound and images

Consider the uppercase and lowercase codes in binary of characters. For example,
‘a’ 1 1 0 0 0 0 1 hex 61 (lower case)

‘A’ 1 0 0 0 0 0 1 hex 41 (upper case)

‘y’ 1 1 1 1 0 0 1 hex 79 (lower case)

‘Y’ 1 0 1 1 0 0 1 hex 59 (upper case)

The above examples show that the sixth bit changes from 1 to 0 when comparing
the lowercase and uppercase of a character. This makes the conversion between
the two an easy operation. It is also noticeable that the character sets (e.g. a to
z, 0 to 9, etc.) are grouped together in sequence, which speeds up usability.
Extended ASCII uses 8-bit codes (0 to 255 in denary or 0 to FF in hexadecimal).
This gives another 128 codes to allow for characters in non-English alphabets and
for some graphical characters to be included:

Figure 1.6 Extended

▲

ASCII code table

27

318281_C01_CAM_IGCSE CO_SCI_001_044.indd 27 18/02/21 3:22 PM

 1 Data representation

ASCII code has a number of disadvantages. The main disadvantage is that it

does not represent characters in non-Western languages, for example Chinese
characters. As can be seen in Figure 1.6 where DOS and Windows use different
characters for some ASCII codes. For this reason, different methods of coding
have been developed over the years. One coding system is called Unicode.
Unicode can represent all languages of the world, thus supporting many
operating systems, search engines and internet browsers used globally. There is
overlap with standard ASCII code, since the first 128 (English) characters are the
same, but Unicode can support several thousand different characters in total.
As can be seen in Table 1.2 and Figure 1.6, ASCII uses one byte to represent a
character, whereas Unicode will support up to four bytes per character.
The Unicode consortium was set up in 1991. Version 1.0 was published with five
goals; these were to:
» create a universal standard that covered all languages and all writing systems
» produce a more efficient coding system than ASCII
Find out more » adopt uniform encoding where each character is encoded as 16-bit or 32-bit
code
DOS appears in the » create unambiguous encoding where each 16-bit and 32-bit value always
ASCII extended code represents the same character
table. Find out what
is meant by DOS and » reserve part of the code for private use to enable a user to assign codes for
why it needs to have an their own characters and symbols (useful for Chinese and Japanese character
ASCII code value. sets, for example).

A sample of Unicode characters are shown in Figure 1.7. As can be seen from the
figure, characters used in languages such as Russian, Romanian and Croatian can
now be represented in a computer).

▲ Figure 1.7 Sample of Unicode characters

28

318281_C01_CAM_IGCSE CO_SCI_001_044.indd 28 18/02/21 3:22 PM

 1.2 Text, sound and images

1.2.2 Representation of sound

Soundwaves are vibrations in the air. The human ear senses these vibrations and
interprets them as sound.
Each sound wave has a frequency, wavelength and amplitude. The amplitude
specifies the loudness of the sound.
High Frequency Wave
Amplitude

Time

Period

Low Frequency Wave

Amplitude

Time

Period

▲ Figure 1.8 High and low frequency wave signals

Sound waves vary continuously. This means that sound is analogue. Computers
cannot work with analogue data, so sound waves need to be sampled in order to
be stored in a computer. Sampling means measuring the amplitude of the sound
wave. This is done using an analogue to digital converter (ADC).
To convert the analogue data to digital, the sound waves are sampled at regular
time intervals. The amplitude of the sound cannot be measured precisely, so
approximate values are stored.
10
9
8
Sound amplitude

7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time intervals

▲ Figure 1.9 A sound wave being sampled

Figure 1.9 shows a sound wave. The x-axis shows the time intervals when the
sound was sampled (1 to 21), and the y-axis shows the amplitude of the sampled
sound to 10.
At time interval 1, the approximate amplitude is 10; at time interval 2, the
approximate amplitude is 4, and so on for all 20 time intervals. Because the
amplitude range in Figure 1.9 is 0 to 10, then 4 binary bits can be used to
represent each amplitude value (for example, 9 would be represented by the

29

318281_C01_CAM_IGCSE CO_SCI_001_044.indd 29 18/02/21 3:22 PM

 1 Data representation

binary value 1001). Increasing the number of possible values used to represent
sound amplitude also increases the accuracy of the sampled sound (for example,
using a range of 0 to 127 gives a much more accurate representation of the
sound sample than using a range of, for example, 0 to 10). The number of bits per
sample is known as the sampling resolution (also known as the bit depth). So,
in our example, the sampling resolution is 4 bits.
Sampling rate is the number of sound samples taken per second. This is
measured in hertz (Hz), where 1 Hz means ‘one sample per second’.
So how is sampling used to record a sound clip?
» the amplitude of the sound wave is first determined at set time intervals (the
sampling rate)
» this gives an approximate representation of the sound wave
» each sample of the sound wave is then encoded as a series of binary digits.

Using a higher sampling rate or larger resolution will result in a more faithful
representation of the original sound source. However, the higher the sampling
rate and/or sampling resolution, the greater the file size.
▼ Table 1.3 The benefits and drawbacks of using a larger sampling resolution when
recording sound

Benefits Drawbacks
larger dynamic range produces larger file size

better sound quality takes longer to transmit/download music files

less sound distortion requires greater processing power

CDs have a 16-bit sampling resolution and a 44.1 kHz sample rate – that is 44 100
Link samples every second. This gives high-quality sound reproduction.
See Section 1.3 for
a calculation of file 1.2.3 Representation of (bitmap) images
sizes. Bitmap images are made up of pixels (picture elements); an image is made up of
a two-dimensional matrix of pixels. Pixels can take different shapes such as:

▲ Figure 1.10

Each pixel can be represented as a binary number, and so a bitmap image is

stored in a computer as a series of binary numbers, so that:
» a black and white image only requires 1 bit per pixel – this means that each pixel
can be one of two colours, corresponding to either 1 or 0
» if each pixel is represented by 2 bits, then each pixel can be one of four colours
(22 = 4), corresponding to 00, 01, 10, or 11
» if each pixel is represented by 3 bits then each pixel can be one of eight colours
(23 = 8), corresponding to 000, 001, 010, 011, 100, 101, 110, 111.
The number of bits used to represent each colour is called the colour depth.
An 8 bit colour depth means that each pixel can be one of 256 colours (because

30

318281_C01_CAM_IGCSE CO_SCI_001_044.indd 30 18/02/21 3:22 PM

 1.2 Text, sound and images

28 = 256). Modern computers have a 24 bit colour depth, which means over
16 million different colours can be represented With x pixels, 2x colours can be
represented as a generalisation. Increasing colour depth also increases the size
of the file when storing an image.
Image resolution refers to the number of pixels that make up an image; for
example, an image could contain 4096 × 3072 pixels (12 582 912 pixels in total).
The resolution can be varied on many cameras before taking, for example, a
digital photograph. Photographs with a lower resolution have less detail than
those with a higher resolution. For example, look at Figure 1.11:

A B C D E

▲ Figure 1.11 Five images of the same car wheel using different resolutions

Image ‘A’ has the highest resolution and ‘E’ has the lowest resolution. ‘E’ has
become pixelated (‘fuzzy’). This is because there are fewer pixels in ‘E’ to
represent the image.
The main drawback of using high resolution images is the increase in file size.
As the number of pixels used to represent the image is increased, the size of
the file will also increase. This impacts on how many images can be stored on,
for example, a hard drive. It also impacts on the time to download an image
from the internet or the time to transfer images from device to device. A certain
amount of reduction in resolution of an image is possible before the loss of
quality becomes noticeable.

Activity 1.15
1 Explain each of the following terms:
i colour depth
ii ASCII code and Extended ASCII code
iii Unicode
iv sampling rate
v bitmap image
2 A colour image is made up of red, green and blue colour combinations. 8 bits
are used to represent each of the colour components.
i How many possible variations of red are there?
ii How many possible variations of green are there?
iii How many possible variations of blue are there?
iv How many different colours can be made by varying the red, green and blue
values?
3 Describe the effect of increasing resolution and sampling rate on the size of a
file being stored in a computer.

31

318281_C01_CAM_IGCSE CO_SCI_001_044.indd 31 18/02/21 3:22 PM