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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.

66

77

Representing ThingsRepresenting Things

Harry

Ken

Tyler

Sue

Xing

88

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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2727

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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.