CH/S5CIT/Nov., 2006.
The representation of data within the computer
Number systems (p. 25 to 28)

Under different number systems, quantities may be represented in different ways.

Different number systems have different numbers of digit symbols. Each digit in a number has its values.
Decimal (Denary)

It is the most familiar one. It originated from counting numbers by fingers.

10 digit symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and each digit has a place value in a power of 10.

e.g. 42810 : digit ‘8’ has a place value 10 0
digit ‘2’ has a place value 10 1
digit ‘4’ has a place value 10 2
Binary
 An electronic pulse is on or off.

The number of meaningful electronic states is only

The most natural coding for computer is binary.

The binary number system has only 2 digit symbols, i.e. 0 and 1, with place values in power of 2.

Conversions
From binary to decimal,
1011102 = 1* 25 + 0 * 24 + 1 * 23 + 1 * 22 + 1 * 21 + 0 * 20 = 4610
From decimal to binary,
2
2
2
2
2
46
23
11
5
2
1
.........
.........
.........
.........
.........
0
1
1
1
0
Therefore, the result is 1011102.
Octal

Programming in binary is however very tedious and prone to error.

The octal system is used as it makes programming simpler (closer to 10) and not very difficult for the
computer (easy conversion between binary and octal).

This system has 8 digit symbols (0 to 7) and each digit has a place value in powers of 8.

Knowing the place values, we can convert octal to decimal and vice versa.
2438 = 2*8 2 + 4*8 1 + 3*8 0 = 16310
8
8
163
20
2
.......3
.......4
i.e. 2438
DATA REPRESENTATION
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CH/S5CIT/Nov., 2006.

Conversions between octal and binary numbers are much simpler, just grouping the binary codes 3 in a
group and then change each group into an octal digit.
e.g. 010 101 0012 = 2518
Hexadecimal

The octal number system has a disadvantage in coding computer instructions. Computers work in twos,
or power of 2, thus it is not efficient for them to deal with numbers in 3-bit groups.

A new number system, the hexadecimal system, is developed with 16 digit symbols (0-9, A-F) and each
hexadecimal digit is equivalent to a 4-digit binary number.
Table represent numbers of different number system
Decimal
Binary
0
1
2
3
4
5
6
7
0000
0001
0010
0011
0100
0101
0110
0111
Hexadecimal
Decimal
0
1
2
3
4
5
6
7
Binary
Hexadecimal
1000
1001
1010
1011
1100
1101
1110
1111
8
9
A
B
C
D
E
F
8
9
10
11
12
13
14
15

Conversions between hexadecimal and binary, and hexadecimal and decimal are similar to those of octal.

Conversions between octal and hexadecimal are done by first converting the number to binary.
Simple Arithmetic on Binary Number
Addition
11
+ 101
0
11
+ 101
00
11
+ 101
000
1010
- 101
1
1010
- 101
01
1010
- 101
101
11
+ 101
1000
Subtraction
Multiplication
110
* 101
11000
110
11110
Division
110
101 )11110
101
1010
1010
Character Set

Characters also stored as binary code in computer.

Usually, one character is stored in 1 byte, so there can be 256 different characters.

The most common character set used in computer is the American Standard Coding for Information
Interchange (ASCII).
DATA REPRESENTATION
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CH/S5CIT/Nov., 2006.
Decimal
Code
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99

Binary
Code
00100000
00100001
00100010
00100011
00100100
00100101
00100110
00100111
00101000
00101001
00101010
00101011
00101100
00101101
00101110
00101111
00110000
00110001
00110010
00110011
01001000
01001001
01001010
01001011
01001100
01001101
01001110
01001111
01010000
01010001
01010010
01010011
01010100
01010101
01010110
01010111
01011000
01011001
01011010
01011011
01011100
01011101
01011110
01011111
01100000
01100001
01100010
01100011
Hexa. Code
Character
20
21
22
23
24
25
26
27
28
29
2A
2B
2C
2D
2E
2F
30
31
32
33
48
49
4A
4B
4C
4D
4E
4F
50
51
52
53
54
55
56
57
58
59
5A
5B
5C
5D
5E
5F
60
61
62
63
(space)
!
"
#
$
%
&
'
(
)
*
+
.
/
0
1
2
3
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
[
\
]
^
_
`
a
b
c
Decimal
Code
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
Binary
Code
00110100
00110101
00110110
00110111
00111000
00111001
00111010
00111011
00111100
00111101
00111110
00111111
01000000
01000001
01000010
01000011
01000100
01000101
01000110
01000111
01100100
01100101
01100110
01100111
01101000
01101001
01101010
01101011
01101100
01101101
01101110
01101111
01110000
01110001
01110010
01110011
01110100
01110101
01110110
01110111
01111000
01111001
01111010
01111011
01111100
01111101
01111110
01111111
Hex
a. Code
34
35
36
37
38
39
3A
3B
3C
3D
3E
3F
40
41
42
43
44
45
46
47
64
65
66
67
68
69
6A
6B
6C
6D
6E
6F
70
71
72
73
74
75
76
77
78
79
7A
7B
7C
7D
7E
7F
Character
4
5
6
7
8
9
:
;
<
=
>
?
@
A
B
C
D
E
F
G
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
x
y
z
{
|
}
~
(del)
Unicode.
i.
It contains the characters from the world’s alphabets, ideographs and symbols.
ii.
Its first 256 codes are the same as that of ASCII.
iii.
The latest version, Unicode 5.0, contains 99020 graphic and format characters. One character may be
stored in 1 byte, 2 bytes or 4 bytes.
DATA REPRESENTATION
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CH/S5CIT/Nov., 2006.
Chinese Text Processing


Under a Chinese text system, we can operate the computer with Chinese characters. That means we
can use the computer to
i.
store the character which represented by certain codes (internal code).
ii.
use the English keyboard to input Chinese characters (input method).
iii.
display the Chinese characters in different shapes (graphical composition of Chinese characters
of different fonts).
All these features are provided by the Chinese operating system. (Windows XP)
Character set

In an English processing system, the internal code of a character may be an ASCII code. E.g. A’s
internal code is ‘01000001’.

In a Chinese processing system, the internal code may be the Chinese National Standard Codes for
Information Interchange, Big 5 or other codes. (The internal code used in Chinese Windows is Big
5.)

In an English processing system, the character set includes the alphabets (‘a’ to ‘z’, and ‘A’ to ‘Z’),
numerals (‘0’ to ‘9’) and symbols, such as ‘$’ , ‘&’, ‘?’, ‘#’, ‘*’, etc, having over 200 characters in
total.

In a Chinese processing system, the character set includes all characters in an English processing
system and all the commonly used Chinese characters, over 10000 in total. The character set is much
larger and thus two bytes are used to store a single Chinese character. (Double Byte Character Set,
DBCS).

Big-5.
i.
For Traditional Chinese characters
ii.
Regions: Taiwan, Hong Kong and Malaysia
iii.


HK government has developed an extension to the set. (Hong Kong Supplementation Character
Set).
GuoBiao (GB).
i.
For Simplified Chinese characters
ii.
Regions: China, Singapore and Malaysia.
Unicode consists of 20902 CJK (Chinese, Japanese and Korean) characters. Thus Simplified Chinese
characters, Traditional Chinese characters and Japanese characters can be identified in athe same
document.
DATA REPRESENTATION
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