Comp201 Computer Systems Data Representation

1
Comp201 Computer SystemsData Representation
2
Data Representation

• Describes the methods by which data can be
  represented and transmitted in a computer.
• Reading Chapter Three Englander

3
Data Representation

• Alphanumeric data
• Big Endian vs Little Endian
• Images
• Bit map
• Vector
• Audio

4
Example Data Representations
5
Alphanumeric Data

• Many applications process text (e.g. compilers
  and word processors)
• coding schemes include ASCII, EBCDIC and Unicode
• ASCII table (in hex)

0
0
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
0
a
0
b
0
c
0
d
0
e
0
f















n
u
l
s
o
h
s
o
t

e
t
x

e
o
t
e
n
q

a
c
k

b
e
l
b
s
h
t
n
l
v
t
n
p
c
r
s
o
s
i
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
1
a
1
b
1
c
1
d
1
e
1
f
















d
l
e
d
c
1
d
c
2
d
c
3
d
c
4
n
a
k
s
y
n
e
t
b
c
a
n
e
m
s
u
b
e
s
c
f
s
g
s
r
s
u
s
2
0
2
1
2
2
2
3
2
4
2
5
2
6
2
7
2
8
2
9
2
a
2
b
2
c
2
d
2
e
2
f
















s
p
!
"




'
(

)


,
-
.
/
3
0
3
1
3
2
3
3
3
4
3
5
3
6
3
7
3
8
3
9
3
a
3
b
3
c
3
d
3
e
3
f
















0
1
2
3
4
5
6
7
8
9


lt

gt
?
4
0
4
1
4
2
4
3
4
4
4
5
4
6
4
7
4
8
4
9
4
a
4
b
4
c
4
d
4
e
4
f
















_at_
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
5
0
5
1
5
2

5
3

5
4

5
5

5
6

5
7

5
8

5
9

5
a

5
b

5
c

5
d

5
e

5
f



P
Q
R
S
T
U
V
W
X
Y
Z

\


_

6
0

6
1

6
2

6
3

6
4

6
5

6
6

6
7

6
8

6
9

6
a

6
b

6
c

6
d

6
e

6
f

a
b
c
d
e
f
g
h
i
j
k
l

m
n
o

7
0

7
1

7
2

7
3

7
4

7
5

7
6

7
7

7
8

7
9

7
a

7
b

7
c
7
d


7
e


7
f
p
q
r
s
t
u
v
w
x
y
z




d
e
l
6

• Characters
• Example what does the following ASCII string
  represent 48 65 6C 6C 6F 20 32 30 31

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Sorting ASCII Characters

• ASCII and EBCDIC codes are designed so the
  computer can do alphabetic comparisons.
• In Windows, comparisons are case insensitive (in
  most instances)
• In Unix comparisons are generally case sensitive

8
EBCDIC codes
Reference Englander, chapter 3
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UNICODE
Greek

• 16 bit code (encode 65536 characters)
• Modelled on ASCII character set
• Encodes most characters currently in use
• Uses scripts to define characters in a particular
  language

Tibetan
Dingbats
Katakana
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Big Endian vs Little Endian

• On most computers the storage unit is a byte
• Multiple bytes are required to store most data
  types (e.g. integers gt 4 bytes)

byte
byte
byte
byte
Address
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Big Endian vs Little Endian

• How do we pack words into a byte addressable
  memory?

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Question Does it matter?

• Answer yes, of course but not much! The
  differences in performance are minor, but (of
  course) you must choose one. Yes, it is possible
  to swap around in software between them.
• Intel processors use Little Endian
• Motorola processors use Big Endian.
• Some programs (e.g.Windows) likewise insist on a
  particular format Windows .bmp format is Little
  Endian, for instance
• Internet protocols are Big Endian. Conversion is
  required on Little Endian processors.

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Some common file formats(reference
www.cs.umass.edu , Dr. William Verts)

• Big Endian
• Adobe Photoshop
• JPEG
• MacPaint
• SGI (silicon graphics)
• Sun Raster
• WPG (word perfect graphics metafile)

• Little Endian
• BMP
• GIF
• PCX (paintbrush)
• QTM (quicktime)
• Microsoft RTF

And some can be either, selected by codes in file
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Pictures

• Many different formats used to store Images in a
  computer
• Two Main categories
• Bit map images
• E.g. photographs paintings
• Characterised by continuous variations
• in shading, colour, shape and texture
• Necessary to store info about each point
• Vector Images
• Made up of geometrical shapes (e.g. lines
  circles etc)
• Sufficient to store geometrical detail plus its
  position

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Bit map Images

• Many different formats
• bit map e.g. GIF, TIFF, ...

Image
Binary Representation
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Bit map storage

• Consider an image with 600 rows of 800 pixels
  one byte used to store each of the three colours
  of each pixel
• Total memory 600 800 3 ? 1.5MB
• Alternative representation is to use a palette
  a lookup table which defines the colours in the
  image
• An index into this table is then stored for each
  pixel
• Can also reduce the size by reducing the
  resolution (I.e. increase the size of each pixel)
  or by employing various compression algorithms (p
  78, 79) to lower storage requirements.

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Example GIF

• Graphics Interchange Format
• A proprietary format developed in 1987
• Gif 89A defn http//www.dcs.ed.ac.uk/home/mxr/gfx
  /2d/GIF89a.txt
• Assumes a rectangular screen containing a number
  of images
• Areas not filled with images are filled with a
  background colour
• Uses a palette to store 256 colours

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Gif Screen
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GIF File Format
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Vector Graphics

• series of objects such as lines and circles e.g.
  PICT, TIFF, ...
• line 0,50,100,50
• line 50,0,50,100
• char A, 75, 25

A
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Example Postscript

• A page description language
• An image consists of a program written in the
  postscript language
• Encoded in ASCII or Unicode
• Contains functions to
• draw lines
• Draw bezier curves
• Join simple object into more complex ones
• Translate or scale an object
• Fill an object

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Figure 3.13 A PostScript program
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Figure 3.14 Another PostScript program
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Audio Data

• Sound is normally digitised from an audio source
• Analog waveform sampled at regular times
  intervals
• The amplitude at each interval is recorded using
  an A-to-D converter
• Most positive peak set max binary number
• Most negative peak set to zero

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Figure 3.15 Digitizing an audio waveform
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Wave (.WAV) Sound format

• Designed by Microsoft
• Supports 8 or 16 bit sound samples
• Sample rates 11.025KHz, 22.05KHz or 44.1KHz
• Supports stereo or mono
• Very simple format

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Wave Format
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Wave Format
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Some statistics

• If we encode sound at 44kHz, each sample at 16
  bits, stereo (2 channels), this amounts to 1.4
  MBits/sec and three minutes will take about 25
  Mbytes of space!
• It we only encode the most important features, it
  is termed data compression, and can reduce file
  size by about 101

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Two popular methods

• Real Audio is one method used for data
  compression.
• MP3 is another.
• Comparative file sizes
• WAV file at 44KHz, 16 bit 5 MB
• Real Audio will take 304KB
• MP3 will take 409KB
• Source www.howstuffworks.com