61A Extra Lecture 4 Announcements Encoding Strings Representing - - PowerPoint PPT Presentation

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61A Extra Lecture 4 Announcements Encoding Strings Representing - - PowerPoint PPT Presentation

Oct 06, 2023 609 likes •1.62k views

61A Extra Lecture 4 Announcements Encoding Strings Representing Strings: UTF-8 Encoding 4 Representing Strings: UTF-8 Encoding UTF (UCS (Universal Character Set) Transformation Format) 4 Representing Strings: UTF-8 Encoding UTF (UCS

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SLIDE 1

61A Extra Lecture 4

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SLIDE 2

Announcements

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SLIDE 3

Encoding Strings

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SLIDE 4

Representing Strings: UTF-8 Encoding

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SLIDE 5

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format)

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SLIDE 6

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers

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SLIDE 7

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes

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SLIDE 8

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255.

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SLIDE 9

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. bytes

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SLIDE 10

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. bytes integers

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SLIDE 11

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. 00000000 bytes integers

4

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SLIDE 12

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. 00000000 00000001 1 bytes integers

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SLIDE 13

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. 00000000 00000001 1 00000010 2 bytes integers

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SLIDE 14

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. 00000000 00000001 1 00000011 3 00000010 2 bytes integers

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SLIDE 15

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. Variable-length encoding: integers vary in the number of bytes required to encode them. 00000000 00000001 1 00000011 3 00000010 2 bytes integers

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SLIDE 16

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. Variable-length encoding: integers vary in the number of bytes required to encode them. 00000000 00000001 1 00000011 3 00000010 2 bytes integers In Python: string length is measured in characters, bytes length in bytes.

4

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SLIDE 17

Representing Strings: UTF-8 Encoding

UTF (UCS (Universal Character Set) Transformation Format) Unicode: Correspondence between characters and integers UTF-8: Correspondence between those integers and bytes A byte is 8 bits and can encode any integer 0-255. Variable-length encoding: integers vary in the number of bytes required to encode them. 00000000 00000001 1 00000011 3 00000010 2 bytes integers In Python: string length is measured in characters, bytes length in bytes.

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(Demo)

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Fixed-Length Encodings

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A First Attempt

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A First Attempt

  • Let’s use an encoding

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SLIDE 21

A First Attempt

  • Let’s use an encoding

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Letter Binary Letter Binary a n 1 b 1

  • c

p 1 d 1 q 1 e 1 r f s 1 g t h 1 u i 1 v 1 j 1 w 1 k x 1 l 1 y m 1 z

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SLIDE 22

Decoding

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SLIDE 23

Decoding

  • An encoding without a deterministic decoding procedure is not very useful

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SLIDE 24

Decoding

  • An encoding without a deterministic decoding procedure is not very useful
  • How many bits do we need to encode each letter uniquely?

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Decoding

  • An encoding without a deterministic decoding procedure is not very useful
  • How many bits do we need to encode each letter uniquely?
  • lowercase alphabet

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Decoding

  • An encoding without a deterministic decoding procedure is not very useful
  • How many bits do we need to encode each letter uniquely?
  • lowercase alphabet
  • 5 bits

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SLIDE 27

A Second Attempt

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SLIDE 28

A Second Attempt

  • Let’s try another encoding

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SLIDE 29

A Second Attempt

  • Let’s try another encoding

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Letter Binary Letter Binary a 00000 n 01101 b 00001

  • 01110

c 00010 p 01111 d 00011 q 10000 e 00100 r 10001 f 00101 s 10010 g 00110 t 10011 h 00111 u 10100 i 01000 v 10101 j 01001 w 10110 k 01010 x 10111 l 01011 y 11000 m 01100 z 11001

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SLIDE 30

Analysis

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SLIDE 31

Analysis

Pros

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SLIDE 32

Analysis

Pros

  • Encoding was easy

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SLIDE 33

Analysis

Pros

  • Encoding was easy
  • Decoding was deterministic

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SLIDE 34

Analysis

Pros

  • Encoding was easy
  • Decoding was deterministic

Cons

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SLIDE 35

Analysis

Pros

  • Encoding was easy
  • Decoding was deterministic

Cons

  • Takes more space…

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SLIDE 36

Analysis

Pros

  • Encoding was easy
  • Decoding was deterministic

Cons

  • Takes more space…
  • What restriction did we place that’s unnecessary?

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SLIDE 37

Analysis

Pros

  • Encoding was easy
  • Decoding was deterministic

Cons

  • Takes more space…
  • What restriction did we place that’s unnecessary?
  • Fixed length

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SLIDE 38

Variable-Length Encodings

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SLIDE 39

Variable Length Encoding

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SLIDE 40

Variable Length Encoding

  • Encoding Candidate 1: A: 1, B:01, C: 10, D: 11, E: 100, F: 101, ...

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Variable Length Encoding

  • Encoding Candidate 1: A: 1, B:01, C: 10, D: 11, E: 100, F: 101, ...
  • What does 01111 encode?

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SLIDE 42

Variable Length Encoding

  • Encoding Candidate 1: A: 1, B:01, C: 10, D: 11, E: 100, F: 101, ...
  • What does 01111 encode?
  • Encoding Candidate 2: A: 00, B: 01, C: 100, D: 101, E: 1100, F: 1101, ...

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SLIDE 43

Variable Length Encoding

  • Encoding Candidate 1: A: 1, B:01, C: 10, D: 11, E: 100, F: 101, ...
  • What does 01111 encode?
  • Encoding Candidate 2: A: 00, B: 01, C: 100, D: 101, E: 1100, F: 1101, ...
  • What does 0100101 encode? How about 10111001101001001100?

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SLIDE 44

Variable Length Encoding

  • Encoding Candidate 1: A: 1, B:01, C: 10, D: 11, E: 100, F: 101, ...
  • What does 01111 encode?
  • Encoding Candidate 2: A: 00, B: 01, C: 100, D: 101, E: 1100, F: 1101, ...
  • What does 0100101 encode? How about 10111001101001001100?
  • Deterministic decoding from left to right is possible if the encoding of one character is

never a proper prefix of the decoding of another character.

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Deterministic Codes Have a Tree Structure

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Deterministic Codes Have a Tree Structure

Letter Binary A 00 B 01 C 1

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SLIDE 47

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Deterministic Codes Have a Tree Structure

1 Letter Binary A 00 B 01 C 1

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SLIDE 48

12

Deterministic Codes Have a Tree Structure

1 C Letter Binary A 00 B 01 C 1

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SLIDE 49

12

Deterministic Codes Have a Tree Structure

1 1 C Letter Binary A 00 B 01 C 1

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SLIDE 50

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Deterministic Codes Have a Tree Structure

1 B 1 C Letter Binary A 00 B 01 C 1

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SLIDE 51

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Deterministic Codes Have a Tree Structure

1 A B 1 C Letter Binary A 00 B 01 C 1

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Huffman Encoding

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Huffman Encoding

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  • Let’s pretend we want to come up with the optimal encoding:
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Huffman Encoding

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  • Let’s pretend we want to come up with the optimal encoding:
  • AAAAAAAAAABBBBBCCCCCCCDDDDDDDDD
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SLIDE 55

Huffman Encoding

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  • Let’s pretend we want to come up with the optimal encoding:
  • AAAAAAAAAABBBBBCCCCCCCDDDDDDDDD
  • A appears 10 times
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Huffman Encoding

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  • Let’s pretend we want to come up with the optimal encoding:
  • AAAAAAAAAABBBBBCCCCCCCDDDDDDDDD
  • A appears 10 times
  • B appears 5 times
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Huffman Encoding

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  • Let’s pretend we want to come up with the optimal encoding:
  • AAAAAAAAAABBBBBCCCCCCCDDDDDDDDD
  • A appears 10 times
  • B appears 5 times
  • C appears 7 times
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Huffman Encoding

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  • Let’s pretend we want to come up with the optimal encoding:
  • AAAAAAAAAABBBBBCCCCCCCDDDDDDDDD
  • A appears 10 times
  • B appears 5 times
  • C appears 7 times
  • D appears 9 times
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SLIDE 59

Huffman Encoding

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Huffman Encoding

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  • Start with the two smallest frequencies
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Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B appears 5 times, C appears 7 times, D appears 9 times
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SLIDE 62

Huffman Encoding

14

  • Start with the two smallest frequencies
  • A appears 10 times, B appears 5 times, C appears 7 times, D appears 9 times

A B C D

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Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B appears 5 times, C appears 7 times, D appears 9 times

A B C D

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Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B appears 5 times, C appears 7 times, D appears 9 times

A B C D 1 A D B C

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Huffman Encoding

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Huffman Encoding

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  • Continue…
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Huffman Encoding

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  • Continue…
  • A appears 10 times, B & C appear a combined 12 times, D appears 9 times
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Huffman Encoding

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  • Continue…
  • A appears 10 times, B & C appear a combined 12 times, D appears 9 times

1 A D B C

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Huffman Encoding

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  • Continue…
  • A appears 10 times, B & C appear a combined 12 times, D appears 9 times

1 A D B C

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Huffman Encoding

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  • Continue…
  • A appears 10 times, B & C appear a combined 12 times, D appears 9 times

1 A D B C 1 B C 1 A D

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Huffman Encoding

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Huffman Encoding

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  • And finally…
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Huffman Encoding

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  • And finally…

1 B C 1 A D

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Huffman Encoding

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  • And finally…

1 B C 1 A D

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Huffman Encoding

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  • And finally…

1 B C 1 A D B D 1 C 1 A 1

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Huffman Encoding

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Huffman Encoding

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  • Another example…
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Huffman Encoding

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  • Another example…
  • AAAAAAAAAABCCD
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Huffman Encoding

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  • Another example…
  • AAAAAAAAAABCCD
  • A appears 10 times
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SLIDE 80

Huffman Encoding

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  • Another example…
  • AAAAAAAAAABCCD
  • A appears 10 times
  • B appears 1 time
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SLIDE 81

Huffman Encoding

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  • Another example…
  • AAAAAAAAAABCCD
  • A appears 10 times
  • B appears 1 time
  • C appears 2 times
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Huffman Encoding

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  • Another example…
  • AAAAAAAAAABCCD
  • A appears 10 times
  • B appears 1 time
  • C appears 2 times
  • D appears 1 time
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Huffman Encoding

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Huffman Encoding

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  • Start with the two smallest frequencies
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Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B appears 1 time, C appears 2 times, D appears 1 time
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SLIDE 86

Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B appears 1 time, C appears 2 times, D appears 1 time

A B C D

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SLIDE 87

Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B appears 1 time, C appears 2 times, D appears 1 time

A B C D

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SLIDE 88

Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B appears 1 time, C appears 2 times, D appears 1 time

A B C D 1 A C B D

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Huffman Encoding

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Huffman Encoding

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  • Start with the two smallest frequencies
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Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B & D appear a combined 2 times, C appears 2 times
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Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B & D appear a combined 2 times, C appears 2 times

1 A C B D

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Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B & D appear a combined 2 times, C appears 2 times

1 A C B D

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Huffman Encoding

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  • Start with the two smallest frequencies
  • A appears 10 times, B & D appear a combined 2 times, C appears 2 times

1 A C B D 1 C 1 B D A

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Huffman Encoding

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Huffman Encoding

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  • And finally…
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Huffman Encoding

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  • And finally…

1 C 1 B D A

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Huffman Encoding

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  • And finally…

1 C 1 B D A

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Huffman Encoding

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  • And finally…

1 C 1 B D 1 A 1 C 1 B D A