Data Representation
Lecture 1
How data are represented in Computer?
• In order to be understood by a computer, data and programs
need to be represented appropriately
• Coding systems: Used to represent data and programs in a
manner understood by the computer
• Computers are made of a series of switches
• Each switch has two states: ON or OFF
• Each state can be represented by a number 1 for “ON” and 0 for
“OFF”
Digital Data Representation
Bit: The smallest unit of data that a binary computer can recognize (a
single 1 or 0)
Byte = 8 bits
Byte terminology used to express the size of documents and other files,
programs, etc.
Digital Data Representation
• Prefixes are often used to express larger quantities of bytes: kilobyte
(KB), megabyte (MB), gigabyte (GB), terabyte (TB), petabyte (PB),
exabyte (EB), zettabyte (ZB), yottabyte (YB).
1 Kilobytes (KB) 210 bytes 1024 bytes
1 Megabytes 220 bytes 1024 KB
(MG)
1 Gegabytes 230 bytes 1024 MB
(GB)
1 Terabytes (TB) 240 bytes 1024 GB
Data vs. Information
• Data
– Raw, unorganized facts
– Can be in the form of text,
graphics, audio, or video
• Information
– Data that has been processed
into a meaningful form
• Information processing
– Converting data into
information
Representing Text
• Each character (letter, punctuation, etc.) is assigned a unique bit
pattern.
• ASCII (American Standard Code for Information Interchange) coding
system traditionally used with personal computers
• Standard ASCII: Uses patterns of 7-bits to represent most symbols used in written
English text
– Extended ASCII: ISO developed a number of 8 bit extensions to ASCII, each
designed to accommodate a major language group
– Unicode: newer code (32 bits per character is common); universal coding
standard designed to represent text-based data written in any ancient or modern
language
Representing Numeric Values
• Numbering System: A way of representing numbers.
• The position of the digits determines the power to which
the base number is raised.
• Binary notation: Uses bits to represent a number in base
two.
Numbering system
Binary Decimal
Bi -> 2 Dec -> 10
base2 base10
Decimal Numbers
• Base=10
• Represented using 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• We use a positional notation system.
• Weight= BasePos
Position Pos 8 Pos 7 Pos 6 Pos 5 Pos 4 Pos 3 Pos 2 Pos 1 Pos 0
Weight 108 107 106 105 104 103 102 101 100
Value 10000000 10000000 1000000 100000 10000 1000 100 10 1
Binary Numbers
• Base=2
• Represented using 2 digits: 0, 1
Position Pos 8 Pos 7 Pos 6 Pos 5 Pos 4 Pos 3 Pos 2 Pos 1 Pos 0 . Pos -1 Pos -2
Weight 28 27 26 25 24 23 22 21 20 . 2-1 2-2
Value 256 128 64 32 16 8 4 2 1 . 0.5 0.25
Converting Base-2 to Base-10
(1 0 0 1 1)
2
OFF
OFF
ON
ON
ON
Exponent:
Calculation:16 0 0 2 1
+ + + + =
(19)10
Decimal to Binary Conversion
Method I:
Use repeated subtraction.
Subtract largest power of 2, then next largest, etc.
Powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2n
Exponent: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 , n
20 21 2 2 23 24 25 26 27 28 29 210 2n
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Decimal to Binary Conversion
• Suppose x = 156410
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Decimal to Binary Conversion
Suppose x = 156410
Subtract 1024: 1564-1024 (210) = 540 n=10 or 1 in the (210)’s position
Subtract 512: 540-512 (29) = 28 n=9 or 1 in the (29)’s position
28=256, 27=128, 26=64, 25=32 > 28, so we have 0 in all of these positions
Subtract 16: 28-16 (24) = 12 n=4 or 1 in (24)’s position
Subtract 8: 12 – 8 (23) = 4 n=3 or 1 in (23)’s position
Subtract 4: 4 – 4 (22) = 0 n=2 or 1 in (22)’s position
Thus:
156410 = (1 1 0 0 0 0 1 1 1 0 0)2
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Decimal to Binary Conversion
Method II:
Use repeated division by radix.
2 | 1564 2|__24_
782
2|_____ R=0 12
2|_____ R=0
2|_____
391 R=0 6
2|_____ R=0
195
2|_____ R=1 3
2|_____ R= 0
97
2|_____ R=1 1
2|_____R=1
2|_____
48 R=1 0 R=1
24 R=0
Collect remainders in reverse order
11000011100
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Representing Graphics
• Graphics (still images
such as photos or
drawings)
– Bitmapped images: A variety of bit
depths are possible (4, 8, 24 bits)
• More bits = more colors
– Graphics Interchange Format (GIF):
GIFs store at most 8 bits per pixel,
so they are limited to 256 colors.
– Joint Photographic Experts Group
(JPEG): Color JPEG images store 24
bits per pixel.
– Portable Network Graphics (PNG):
GIF files can use only 1, 2, 4, or 8
bits per pixel.
Representing Audio and Video Data
• Audio data: Must be in digital form in order to be stored on or
processed by a computer
– Often compressed when sent over the Internet
• MP3 files
• Video data: Displayed using a collection of frames, each frame contains
a still image
– Amount of data can be substantial, but can be compressed
– Developers keep on defining new formats aiming for more quality
with less space.
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