Transcript Data as the computer sees it

Data as the
computer sees it
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Number
systems
Data storage
Glossary
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Because of their electronics, computers
work with only two states – on or off, that is
a binary or base 2 number system
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Base 10
(Decimal)
2358
Base 2 (Binary)
10101012
Base 16
(Hexadecimal)
A2CD3E16
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Decimal number (base 10): 4192.304
Number
4
1
9
2
Placeholde
r column
3
2
1
Place
value/
Written as
base
103
102
1000
100
Place
value
Expanded
notation
.
3
0
4
0
-1
-2
-3
101
100
10-1
10-2
10-3
10
1
1/10
=0,1
1/100 1/1000
=0,01 =0,001
4192.304
=4 X 103+1 X 102+9 X 101+2X100+3X10-1+0X10-2+4X10-3
=4000+100+90+2+0.3+0+0.004
=4192.304
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Binary number (base 2): 1101.101
Example of
number
1
1
0
1
Placeholder
column
3
2
1
Place value
written as
23
22
4
.
1
0
1
0
-1
-2
-3
21
20
2-1
2-2
2-3
2
1
½
¼
1/8
=0.5
=0.25 =0.125
Base Placeholder
column
Place value (as 8
a decimal
value)
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Hexadecimal numbers (base 16)
Example of
number
1
A
5
F
Placeholder
column
3
2
1
Place value
written as
163
162
4096
256
.
3
D
0
-1
-2
161
160
16-1
16-2
16
1
1/16
1/256
Base Placeholder
column
Place value (as a
decimal value)
=0.0625 =0.00390625
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


Engineers discovered that it was easy, from a ‘physical’,
engineering point of view, to have just two states – on
or off.
This could easily be represented by the presence or
absence of current flow.
Hence at the lowest level, data is represented in binary,
to make it easier to design and build hardware.
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Convert binary numbers to decimal numbers
10012= (1 x 23) + (0 x 22) + (0 x 21) + (1 x 20)
= (1 x 8) + (0 x 4) + (0 x 2) + (1 x 1)
=8+1
=9
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Convert the following binary numbers to decimal numbers,
showing all your calculations.
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Convert hexadecimal to decimal number
2F316= (2 x 162) + (F x 161) + (3 x 160)
= (2 x 256) + (15 x 16) + (3 x 1)
= 512 + 240 + 3
= 755
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Convert the following hexadecimal numbers to decimal,
showing all your calculations.
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This is good old
primary school
division with
the remainder!
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Convert the following decimal numbers to binary numbers.
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634 ÷ 16 = 39 remainder 10
39 ÷ 16 = 2 remainder 7
2
÷ 16 = 0 remainder 2
answer is 27A16 (10 = A)
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Write the following decimal numbers in hexadecimal notation.
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


Each of these data types is allocated a fixed number
of what is termed bytes.
Each byte (a number in binary format e.g.
101100112) in turn, consists of 8 binary digits or bits.
Here is an example of data stored in 4 bytes of 8 bits
each, i.e. 32 bits.
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Common
data types:
Integer or
whole
number
Real or
decimal or
floating point
String or text
 Each
data type is
allocated a fixed amount
of space (bytes) to store
its associated data
 There
is therefore a limit
on the data that can be
stored –more bytes larger the range and
fewer bytes - smaller the
range.
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Delphi
Data
type
Bytes
allocated
Java
Range
Data
type
Bytes
allocated
Range
byte
1
0..255
byte
1
-128 to127
Short
int
2
-32768 .. 32767
short
2
-32768 .. 32767
-2147483648..
int
4
-2147483648..
integer 4
2147483647
int64
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-9223372036854
775808..
922337203685477
5807
2147483647
long
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-92233720368
54775808..
9223372036854
775807
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A
text or string variable that could store a
maximum of 5 characters and was assigned
the value ‘Addendum’ to the variable.
A
 Some
d
d
e
n
of the text can be ‘lost’.
 We
refer to the situation where an integer
number is ‘misrepresented’ due to an
insufficient number of bits being available,
as overflow.
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

Each program/programming language uses
different numbers of bytes to store numbers
Decimal or real numbers are normally stored in
two parts, namely a ‘number’ part and an
‘exponent’ part e.g. 3.1415462973812 x 1012

Obviously, a loss of accuracy in the exponent
part would be critical !

A loss of accuracy in the number part would lead
to a loss of accuracy in the number of decimals
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 Coding
schemes
 The
ASCII system was the original
standard which assigned numeric values
to letters, digits, punctuation marks, and
other characters
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


Pictures and sound clips
Picture is a collection of
thousands of dots, each of which
can be modelled by
representing its position and
colour etc.,then we can digitise
any picture or video
Music too can be modelled by
representing the data as
numerical values describing
volume, pitch and frequency
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Know the basics
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Apply your knowledge
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Think and research
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ASCII
Binary
Bit
Byte
Coding
scheme
Decimal
Hexadecimal
Octal
Overflow
Primitive
data type
Truncation
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