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Digitizing Discrete Information

Digitizing Discrete Information. Digitize Represent info with digits (symbols) Digits: { 0, 1, 2, …, 9 } Or digits: { A, B, C, …, Z } Or any set of distinct symbols. Symbols, Briefly. Prefer short names for symbols One, two, …, Instead of “asterisk”, “closing parenthesis”, etc.

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Digitizing Discrete Information

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  1. Digitizing Discrete Information • Digitize • Represent info with digits (symbols) • Digits: { 0, 1, 2, …, 9 } • Or digits: { A, B, C, …, Z } • Or any set of distinct symbols

  2. Symbols, Briefly • Prefer short names for symbols • One, two, …, • Instead of “asterisk”, “closing parenthesis”, etc. • Aside: we shorten many names in IT • exclamation point => bang • asterisk => star • open parenthesis => open paren • open curly brace => open brace

  3. Ordering Symbols • Want order for the digits/symbols • 0 – 9 has obvious order • But what about { !, @, #, …, ) }? • Define acollating sequence • Digitize • Represent info with symbols

  4. Fundamental Information Representation • Given digital info, how to store it? • Use physical phenomena • Light • Current • Magnetism

  5. Fundamental Information Representation • In digital world • Don’t care how much, just presence • In logical world (basis of computing) • True and false

  6. Fundamental Information Representation • Physical world can implement logical world • Presence => “true” • Absence => “false”

  7. The PandA Representation • We will use “PandA” for presence and absence representation • Only two states • Could use false for absent, true for present • Or 0 for absent, and 1 for present

  8. The PandA Representation • Such a formulation is said to be discrete • Discrete means “distinct” or “separable” • Opposite of continuous • No “shadesof gray”

  9. Analog vs. Digital Analog is continuous data/information Sound waves

  10. Analog vs. Digital Digital is discrete info Obtained by sampling

  11. A Binary System • PandA encoding is binary

  12. Bits Form Symbols • PandA unit is a binary digit (bit) • Bit sequences form binary numbers

  13. Encoding Bits on a CD-ROM PandAbit values are pits and lands

  14. Bits in Computer Memory • Memory is a long sequence of bits • Sidewalk Analogy

  15. Sidewalk Memory • Imagine clean sidewalk consisting of squares • Presence of a stone on a square => 1 • Absence of a stone => 0 • Sidewalk: sequence of bits

  16. Sidewalk Memory 0 1 0 0 0 1 0 1

  17. Sidewalk Memory • Writing info • Put stone on square (1) • Remove stone from square (0) • Reading info

  18. Alternative PandA Encodings • Other ways to encode two states • Color of stone • Number of stones • Another?

  19. Combining Bit Patterns • One bit with two states isn’t enough • So we combine them

  20. Hex Explained • Hex numbers are base-16 • A bit sequence may be 1111111110011000111000101010 • Error prone • Instead use hex

  21. The 16 Hex Digits • Hex digits • { 0, 1, 2, …, 9, A, B, C, D, E, F } • Can represent 4-bit sequences • 0000 = 0 hex • 0001 = 1 hex • … • 1001 = 9 hex • 1010 = A hex • … • 1111 = F hex

  22. Hex to Bits and Back Again • Each hex digit corresponds to 4 bits • 0010 1011 1010 1101 2 B A D • F A B 41111 1010 1011 0100 • 1 9 C 6 ?

  23. Digitizing Numbers in Binary • Need binary representations for • Numbers • Characters • But also • image • video • sound

  24. Counting in Binary • Binary numbers (base 2) uses digits 0 and 1 • Decimal numbers (base 10) use 0 through 9 Counting to ten

  25. Counting in Binary • Place value representation

  26. Place Value in a Decimal Number • Example, 1010 (base 10) is (1 × 1000) + (0 × 100) + (1 × 10) + (0 × 1)

  27. Place Value in a Binary Number • Binary is base 2so powers of 2 are used

  28. Place Value in a Binary Number • 1010 in binary • (1 × 8) + (0 × 4) + (1 × 2) + (0 × 1)

  29. Digitizing Text • # of bits determines # of symbols that can be represented • n bits => 2n symbols

  30. Digitizing Text • To digitize English text • Roman letters • Arabic numbers • Punctuation • Arithmetic symbols

  31. Assigning Symbols • So we need to represent • 26 uppercase • 26 lowercase letters • 10 numerals • 20 punctuation characters • 10 arithmetic characters • 3 other characters (new line, tab, and backspace) • 95 symbols…enough for English

  32. Assigning Symbols • To represent 95 distinct symbols we need how many bits? • Need to represent control characters too

  33. Assigning Symbols • ASCII stands for American Standard Code for Information Interchange • Widely used 7-bit code • Advantages of a “standard” • Interoperability of h/w • Communications among programs

  34. Extended ASCII: An 8-Bit Code • For other languages 7 bits aren’t enough • IBM developed an 8-bit ASCII • Uses 1 byte • Uses 0 in leftmost bit followed by 7-bit ASCII codes • Allows 128 more codes that start with 1 • Can handle most Western languages

  35. ASCII Character Set (Decimal) Decimal - Character 0 NUL 1 SOH 2 STX 3 ETX 4 EOT 5 ENQ 6 ACK 7 BEL 8 BS 9 HT 10 NL 11 VT 12 NP 13 CR 14 SO 15 SI 16 DLE 17 DC1 18 DC2 19 DC3 20 DC4 21 NAK 22 SYN 23 ETB 24 CAN 25 EM 26 SUB 27 ESC 28 FS 29 GS 30 RS 31 US 32 SP 33 ! 34 " 35 # 36 $ 37 % 38 & 39 ' 40 ( 41 ) 42 * 43 + 44 , 45 - 46 . 47 / 48 0 49 1 50 2 51 3 52 4 53 5 54 6 55 7 56 8 57 9 58 : 59 ; 60 < 61 = 62 > 63 ? 64 @ 65 A 66 B 67 C 68 D 69 E 70 F 71 G 72 H 73 I 74 J 75 K 76 L 77 M 78 N 79 O 80 P 81 Q 82 R 83 S 84 T 85 U 86 V 87 W 88 X 89 Y 90 Z 91 [ 92 \ 93 ] 94 ^ 95 _ 96 ` 97 a 98 b 99 c 100 d 101 e 102 f 103 g 104 h 105 i 106 j 107 k 108 l 109 m 110 n 111 o 112 p 113 q 114 r 115 s 116 t 117 u 118 v 119 w 120 x 121 y 122 z 123 { 124 | 125 } 126 ~ 127 DEL

  36. ASCII Character Set (Hexadecimal) Hexadecimal - Character 00 NUL 01 SOH 02 STX 03 ETX 04 EOT 05 ENQ 06 ACK 07 BEL 08 BS 09 HT 0A NL 0B VT 0C NP 0D CR 0E SO 0F SI 10 DLE 11 DC1 12 DC2 13 DC3 14 DC4 15 NAK 16 SYN 17 ETB 18 CAN 19 EM 1A SUB 1B ESC 1C FS 1D GS 1E RS 1F US 20 SP 21 ! 22 " 23 # 24 $ 25 % 26 & 27 ' 28 ( 29 ) 2A * 2B + 2C , 2D - 2E . 2F / 30 0 31 1 32 2 33 3 34 4 35 5 36 6 37 7 38 8 39 9 3A : 3B ; 3C < 3D = 3E > 3F ? 40 @ 41 A 42 B 43 C 44 D 45 E 46 F 47 G 48 H 49 I 4A J 4B K 4C L 4D M 4E N 4F O 50 P 51 Q 52 R 53 S 54 T 55 U 56 V 57 W 58 X 59 Y 5A Z 5B [ 5C \ 5D ] 5E ^ 5F _ 60 ` 61 a 62 b 63 c 64 d 65 e 66 f 67 g 68 h 69 i 6A j 6B k 6C l 6D m 6E n 6F o 70 p 71 q 72 r 73 s 74 t 75 u 76 v 77 w 78 x 79 y 7A z 7B { 7C | 7D } 7E ~ 7F DEL

  37. Beyond ASCII Unicode Uses up to 4 bytes to handle how many characters? Allows all modern scripts (Kanji, Arabic, Cyrillic, Hebrew, etc.) Contains 8-bit ASCII as the low 256 characters for compatibility Allows ancient scripts like Egyptian hieroglyphics

  38. ASCII Coding of Phone Numbers How to encode 888 555 1212 in ASCII? Encode each digit with its ASCII byte 8 8 8 5 5 etc. 00111000 00111000 00111000 00110101 00110101 etc.

  39. Another ASCII Example • From Lab 1 CSCI ftw! Takes ? bytes to store. Representation in ASCII? 43 53 43 49 20 66 74 77 21 0A In Binary? 0100 0011 0101 0011 0100 0011 0100 1001 ... 0010 0001 0000 1010

  40. Advantages of Long Encodings • Short encodings save memory • Examples of longer encodings • NATO Broadcast Alphabet • Bar Codes

  41. NATO Broadcast Alphabet • NATO alphabet • Used for radio communication • Purposely inefficient • Distinctive amid noise (‘m’ versus ‘n’) • Letters represented with word “symbols” • a => alpha, b => bravo, c => charlie • Digits keep their usual names • Except 9 => niner

  42. NATO Broadcast Alphabet

  43. Bar Codes • Universal Product Codes (UPC) use more bits than necessary • UPC-A encoding uses 7 bits to encode the digits 0 – 9

  44. Bar Codes • Encodes manufacturer (left side) and product (right side) • Different bit combinations are used for each side • One side is complement of the other • Bit patterns were chosen to appear as different as possible

  45. Bar Codes • Encodings for each side make it possible to recognize whether code is upside down

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