Chapter 1
INFORMATION REPRESENTATION
,M.S.O
Introduction
Numbering System
Measurement of the size of computer memories
Uses of the hexadecimal system
Signed Integers ( positive and Negative)
Contents
Binary Coded Decimal
Images
Sound
Video
Compression
, M.S.O
Numbering System
• Denary System
Human are all familiar with the
denary (base 10) number system
which counts in multiples of 10.
This gives us the well-known
headings of units, 10s, 100s, 1000s
and so on
• Binary System
Based on the number 2. Thus, only
the two ‘values’ 0 and 1 can be
used in this system to represent
each digit. Using the same method
as denary, this gives the headings of
1, 2, 4, 8 and so on.
, M.S.O
Numbering System
• Hexa-Decimal System
Very closely related to the binary
system. Hexadecimal (sometimes
referred to as simply ‘hex’) is a base
16 system and therefore needs to
use 16 different ‘values’ to
represent each digit.
Because it is a system based on 16
different digits, the numbers 0 to 9
and the letters A to F are used to Since 16 = 24 this means that FOUR binary digits are equ
represent each hexadecimal (hex) to each hexadecimal digit.
digit. (A = 10, B = 11, C = 12, D = 13,
E = 14 and F = 15.)
,M.S.O
Conversions : Binary to Denary
What is the denary value of the following binary number?
11101110
1 1 1 0 1 1 1 0
27 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
2+4+8+32+64+128= 238
The Answer is : 238
,M.S.O
Conversions : Binary to Denary
What is the denary value of the following binary number?
Activ
10100011
The Answer is :
,M.S.O
Conversions : Denary to Binary
What is the Binary value of the following denary number
115
128 64 32 16 8 4 2 1
0 1 1 1 0 0 1 1
128 > 115-64 51-32 = 19-16= 3 8>3 4>3 3-2 =1 1-1=0
115 =51 19
01110011
The Answer is : 01110011
,M.S.O
Conversions : Denary to Binary
What is the Binary value of the following denary number Activ
250
The Answer is :
,M.S.O
Conversions : Hexa-Decimal
• Hexa-Decimal Digits
Denary Hexa-Decimal
0-9 0-9
10 A
11 B
12 C
13 D
14 E
15 F
, M.S.O
Conversions : Hexa-Decimal
Denary 230
230
128 64 32 16 8 4 2
1 1 1 0 0 1 1
Binary
8 4 2 1 8 4 2
11100110
2+4+8 = 14 2+4 = 6
E 6
Hexa-Decimal
E6 E6
INFORMATION REPRESENTATION
,M.S.O
Introduction
Numbering System
Measurement of the size of computer memories
Uses of the hexadecimal system
Signed Integers ( positive and Negative)
Contents
Binary Coded Decimal
Images
Sound
Video
Compression
, M.S.O
Numbering System
• Denary System
Human are all familiar with the
denary (base 10) number system
which counts in multiples of 10.
This gives us the well-known
headings of units, 10s, 100s, 1000s
and so on
• Binary System
Based on the number 2. Thus, only
the two ‘values’ 0 and 1 can be
used in this system to represent
each digit. Using the same method
as denary, this gives the headings of
1, 2, 4, 8 and so on.
, M.S.O
Numbering System
• Hexa-Decimal System
Very closely related to the binary
system. Hexadecimal (sometimes
referred to as simply ‘hex’) is a base
16 system and therefore needs to
use 16 different ‘values’ to
represent each digit.
Because it is a system based on 16
different digits, the numbers 0 to 9
and the letters A to F are used to Since 16 = 24 this means that FOUR binary digits are equ
represent each hexadecimal (hex) to each hexadecimal digit.
digit. (A = 10, B = 11, C = 12, D = 13,
E = 14 and F = 15.)
,M.S.O
Conversions : Binary to Denary
What is the denary value of the following binary number?
11101110
1 1 1 0 1 1 1 0
27 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
2+4+8+32+64+128= 238
The Answer is : 238
,M.S.O
Conversions : Binary to Denary
What is the denary value of the following binary number?
Activ
10100011
The Answer is :
,M.S.O
Conversions : Denary to Binary
What is the Binary value of the following denary number
115
128 64 32 16 8 4 2 1
0 1 1 1 0 0 1 1
128 > 115-64 51-32 = 19-16= 3 8>3 4>3 3-2 =1 1-1=0
115 =51 19
01110011
The Answer is : 01110011
,M.S.O
Conversions : Denary to Binary
What is the Binary value of the following denary number Activ
250
The Answer is :
,M.S.O
Conversions : Hexa-Decimal
• Hexa-Decimal Digits
Denary Hexa-Decimal
0-9 0-9
10 A
11 B
12 C
13 D
14 E
15 F
, M.S.O
Conversions : Hexa-Decimal
Denary 230
230
128 64 32 16 8 4 2
1 1 1 0 0 1 1
Binary
8 4 2 1 8 4 2
11100110
2+4+8 = 14 2+4 = 6
E 6
Hexa-Decimal
E6 E6
