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Harvard University CSCI E-2a Life, Liberty, and Happiness After the Digital Explosion. 3A: Data Representation. Representation. How do you represent “things” with bits Anything Text Documents Pictures Sounds. Representation. How do you represent “things” with bits - PowerPoint PPT Presentation
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Harvard UniversityCSCI E-2a
Life, Liberty, and Happiness
After the Digital Explosion
Harvard UniversityCSCI E-2a
Life, Liberty, and Happiness
After the Digital Explosion
3A: Data Representation3A: Data Representation
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RepresentationRepresentation
• How do you represent “things” with bits• Anything
• Text• Documents
• Pictures• Sounds
• How do you represent “things” with bits• Anything
• Text• Documents
• Pictures• Sounds
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RepresentationRepresentation
• How do you represent “things” with bits
• Why does representation matter?
• How do you represent “things” with bits
• Why does representation matter?
Power
Money
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Bits (“Binary digITs”)Bits (“Binary digITs”)
• There are two bits: 0 and 1• Everything else is a sequence of
bits • I.e. a “bit string”• 0010101, 111100010100101011
• There are two bits: 0 and 1• Everything else is a sequence of
bits • I.e. a “bit string”• 0010101, 111100010100101011
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Digital representations are, by definition,
approximations.
They leave out a lot.
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Representing ThingsRepresenting Things
Harry
Ken
Tyler
Sue
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Representing ThingsRepresenting Things
Harry 1
Ken 2
Tyler 3
Sue 4
Xing 5
99
Representing ThingsRepresenting Things
Harry 1 0
Ken 2 1
Tyler 3 ?
Sue 4
Xing 5
1010
Representing ThingsRepresenting Things
Harry 1 0 00
Ken 2 1 01
Tyler 3 ? 10
Sue 4 11
Xing 5 ??
1111
Representing ThingsRepresenting Things
Harry 1 0 00 000
Ken 2 1 01 001
Tyler 3 ? 10 010
Sue 4 11 011
Xing 5 ?? 100
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How many bits for “n” thingsHow many bits for “n” things
• Each bit doubles the number• 1 bit = 2, 2 bits = 4, 3 bits = 8• N bits = 2n things• 10 bits = 1024 etc.
• Each bit doubles the number• 1 bit = 2, 2 bits = 4, 3 bits = 8• N bits = 2n things• 10 bits = 1024 etc.
Another example of exponential growth
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How many bits does it take to represent the 2007
Red Sox Season?
How many bits does it take to represent the 2007
Red Sox Season?
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Red Sox 2007Red Sox 2007
• 162 games = 162 bits (96 “1”s and 66 “0”s
• Add 4 bits / game for opponent• Add Inning results• Add at-bat results• Add pitch details• Stop when you’ve had enough
• 162 games = 162 bits (96 “1”s and 66 “0”s
• Add 4 bits / game for opponent• Add Inning results• Add at-bat results• Add pitch details• Stop when you’ve had enough
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Representing TextRepresenting Text
• 8 bits per character• “A” = 01000001• “(” = 00101000• How many combinations of 8 bits?
2· 2· 2· 2· 2· 2· 2· 2 = 28 = 256
• 8 bits per character• “A” = 01000001• “(” = 00101000• How many combinations of 8 bits?
2· 2· 2· 2· 2· 2· 2· 2 = 28 = 256
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Hexadecimal DigitsHexadecimal Digits
0000 0001 0010 0011 0100 0101 0110 0111
0 1 2 3 4 5 6 7
1000 1001 1010 1011 1100 1101 1110 1111
8 9 A B C D E F
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xy
0 1 2 3 4 5 6 7 8 9 A B C D E F
0
1
2 sp ! " # $ % & ' ( ) * + , - . /
3 0 1 2 3 4 5 6 7 8 9 : ; < = > ?
4 @ A B C D E F G H I J K L M N O
5 P Q R S T U V W X Y Z [ \ ] ^ _
6 ` a b c d e f g h i j k l m n o
7 p q r s t u v w x y z { | } ~ del
ASCIIAmerican Standard Code for Information
InterchangeCharacter represented by Hex xy, e.g. 4B is “K”
ASCIIAmerican Standard Code for Information
InterchangeCharacter represented by Hex xy, e.g. 4B is “K”
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ASCII UnderneathASCII Underneath
• Emails• Web pages
• Emails• Web pages
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What if you need more than 256 characters?
What if you need more than 256 characters?
• Unicode• 32 bits per character (roughly 4
billion different characters)
• Unicode• 32 bits per character (roughly 4
billion different characters)
2020
2121
2222
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What about documents?What about documents?
Representation+
Interpretation
Representation+
Interpretation
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Word ProcessorsWord Processors602PC SuiteAppleWorksApplix Word -Atlantis Ocean MindEasyWordFrameMakerHan/GulLotus Word ProMellelMicrosoft Word -Nisus Writer -Pages -Papyrus – PolyEditStarOfficeTextMakerWordExpressWordPerfectHieroglyphJarteMadhyamAmíAtariWriter BravoBank Street WriterDeskMate
DisplayWriteDocument EditorEasyWriterFullWrite Professional geoWriteGypsylexiconLocoScriptMacWriteMagic WandMindWrite MultiMatePaperClippfs:WriteProtextSpeedScriptSprintTasteTJ-2 [3]TranswriteWordMARCWordStarWordsworth WriteNow XyWrite
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Why not pick one?Why not pick one?
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Why representation mattersWhy representation matters
• Loss of data and the inability to exchange is the primary deterrent to switching vendors.
• Control the representation and your control what can be seen and what can be done.
• Loss of data and the inability to exchange is the primary deterrent to switching vendors.
• Control the representation and your control what can be seen and what can be done.
