Transcript Document
Comp201 Computer Systems
Data Representation
1
Data Representation
Describes the methods by which data can be
represented and transmitted in a computer.
Reading: Chapter Three – Englander
2
Data Representation
Alphanumeric data
Big Endian vs Little Endian
Images
Bit map
Vector
Audio
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Example Data Representations
Type
Standard
Alphanumeric
ASCII,EBCDIC, Unicode
Image(bit map)
GIF,PCX,TIFF,BMP
Image (object)
PICT, Postscript
Sound
WAV, AVI,MP3,MIDI
Page description
PDF, HTML
Video
Quicktime,MPEG2,Real
Video
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Alphanumeric Data
00
nul
10
dle
20
sp
30
0
40
@
50
P
60
`
70
p
Many applications process text (e.g. compilers and
word processors)
coding schemes include ASCII, EBCDIC and Unicode
ASCII table (in hex)
01
soh
11
dc1
21
!
31
1
41
A
51
Q
61
a
71
q
02
sot
12
dc2
22
"
32
2
42
B
52
R
62
b
72
r
03
etx
13
dc3
23
#
33
3
43
C
53
S
63
c
73
s
04
eot
14
dc4
24
$
34
4
44
D
54
T
64
d
74
t
05
enq
15
nak
25
%
35
5
45
E
55
U
65
e
75
u
06
ack
16
syn
26
&
36
6
46
F
56
V
66
f
76
v
07
bel
17
etb
27
'
37
7
47
G
57
W
67
g
77
w
08
bs
18
can
28
(
38
8
48
H
58
X
68
h
78
x
09
ht
19
em
29
)
39
9
49
I
59
Y
69
i
79
y
0a
nl
1a
sub
2a
*
3a
:
4a
J
5a
Z
6a
j
7a
z
0b
vt
1b
esc
2b
+
3b
;
4b
K
5b
[
6b
k
7b
{
0c
np
1c
fs
2c
,
3c
<
4c
L
5c
\
6c
l
7c
0d
cr
1d
gs
2d
3d
=
4d
M
5d
]
6d
m
7d
}
0e
so
1e
rs
2e
.
3e
>
4e
N
5e
^
6e
n
7e
~
0f
si
1f
us
2f
/
3f
?
4f
O
5f
_
6f
o
7f
del 5
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
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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
0
7
On most computers the
storage unit is a byte
100
byte
101
byte
102
byte
103
byte
Address
Multiple bytes are required to store most data
types (e.g. integers => 4 bytes)
MSB
31
LSB
24 23
16 15
8 7
0
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Big Endian vs Little Endian
How do we pack words into a byte addressable memory?
MSB
31
Big Endian
24 23
16 15
8 7
0
Little Endian
0
7
100
LSB
MSB
100
101
101
102
102
103
LSB
0
7
103
LSB
MSB
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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
176.0"
Made up of geometrical shapes
(e.g. lines circles etc)
Sufficient to store geometrical
detail plus its position
251.2"
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Bit map Images
Many different formats:
bit map e.g. GIF, TIFF, ...
Image:
Binary
Representation:
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
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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,
...
A
line 0,50,100,50
line 50,0,50,100
char A, 75, 25
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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
Length of
Chunk
Chunk ID
R
I
F
F
W A V E
DATA
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Wave Format
Length of
Chunk
Chunk ID
R
I
F
W A V E
F
Format Chunk
f
m t
DATA
Data Chunk
10 00 00 00 01 00
Length of
Format
Chunk
Always (0x10)
Always (0x01)
Sample Rate
(Binary, in Hz)
Channel Numbers
(Always 0x01=Mono,
0x02=Stereo)
Bytes Per
Second
Bits Per
Sample
Bytes Per Sample:
1=8 bit Mono,
2=8 bit Stereo or 16 bit Mono,
4=16 bit Stereo
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Wave Format
Length of
Chunk
Chunk ID
R
I
F
F
W A V E
Format Chunk
d
a t
a
DATA
Data Chunk
Data
Length of
data
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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 10:1
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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
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