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2. Discrete / Continuous Representations Of numbers – binary & decimal Bits Hexadecimal - 'Hex' Representing text Bits and Bytes

3. 3 By the end of this lecture you should … Have an awareness of –What digits, bits and bytes are –What 'digitizing' is –What 'hex' is, why it is used and how to use it –What ASCII and Unicode are Understand better how computers represent information

4. Discrete / Continuous Representations Of numbers – binary & decimal Bits Hexadecimal - 'Hex' Representing text Bits and Bytes

5. 5 Discrete vs Continuous Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

6. 6 Discrete vs Continuous  Some things have a continuous range of values. Light and color for example have varying hues or range of intensities.  Clicking and drumming are discrete. Humming and whistling are continuous.

7. Analogue Digital 7 FreeFoto.com

8. 8 Analogue and digital  Digital storage is discrete  Analogue storage is continuous  Digital processing is carried out through discrete specified steps  Analogue processing is uses the physical properties of objects and processes to model

9. Discrete / Continuous Representations Of numbers – binary & decimal Bits Hexadecimal - 'Hex' Representing text Bits and Bytes

10. 10 Numbers What is a number  Numbers are things that we count with  Numbers have an order  We add numbers together to get other numbers. Something that we use numerals to represent numbers  (Numerals - 'arabic' 'roman' 'chinese‘)

11. 11 Symbols represent numbers Different shapes, different words, different symbols one ONE one one one 1 1 Roman numerals I and i Chinese characters Zero 0 What ІІ represents depends on the context

12. 12 Human number systems  Roman system (every so often need a new symbol) I II III IV V VI VII VIII IX X ID D DI IL L LI IM M MI  Base ten (ours, Arabic, Indian, …) 0 1 2 3 4 5 6 7 8 9 (don’t need new symbols) 10 100 1000 10000 100000 … decimal system (positional base 10)

13. 13 Number systems  Base "two" – uses two symbols = Binary These symbols could be almost anything Could be written with zeros and ones – 0 and 1  Base "ten" – uses ten symbols = Decimal could be written with using our usual numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

14. 14 Between Machines & end-users  Machines use binary representations internally (It's fast, convenient, easy direct and useful) For end users, machines are designed to convert to the standard representation (0,1,2,3,4,5,6,7,8,9)

15. 15 Digitising Discrete Information  Digitise – to represent information with digits  Digitise originally meant using the ten numerals ‘0’ through ‘9’  Telephone numbers, National Insurance numbers, etc. are examples of digitised information.

16. 16 Machines and People Computing machines {nowadays} manipulate 0s and 1s Deep in a computer everything is 0s and 1s Computer programs Computer data People 'manipulate' Numbers Words Images Words – spoken language ‘Images’ (symbols) used to represent spoken language (either to

17. 17 For computers  Computers (internally) represent everything as binary (eg as 0 and 1) Everything means everything – text, sound, images, computer programmes … If a computer is used to search through a database and find all those people whose name begins with the letter "G", the most basic representation of the letter G is as some sequence of 0s and 1s

18. 18 “bits are bits” The same 4 bytes shown can be interpreted differently depending on context. Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

19. 19 For people  Long (or even relatively short 7±2) sequences of 0s and 1s are very hard for us to read, write, remember, check, communicate with …  We can make quick and easy use of a large number of discrete symbols (but we need to limit the number of symbol chunks that we are handling at any one time)

20. 20 Ordering Symbols  One advantage of using digits for encoding is that they can be listed in numerical order.  Not always used, however, such as in a telephone book, where listing is by name.  If you use symbols other than digits, you would have to decide on an ordering sequence, called “collating sequence”.

21. Discrete / Continuous Representations Of numbers – binary & decimal Bits Hexadecimal - 'Hex' Representing text Bits and Bytes

22. 22 Bits For Symbols  Bit stands for binary digit. –A bit is single item of binary information – We can think of a bit as a single zero or a single one (in some forms of computer memory – it could the presence or absence of an electrical charge at a specific location – it could be the presence or absence of a magnetic charge at a location

23. Discrete / Continuous Representations Of numbers – binary & decimal Bits Decimal and binary again Hexadecimal - 'Hex' Representing text Bits and Bytes

24. 24 n bits2n2n Represent 12121 2 22 4 32323 8 42424 16 52525 32 62626 64 72727 128 82828 256 92929 512 102 10 1024 A picture will help!

25. 25 The decimal number 1010 representing one thousand ten = 10 + 1000. Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

26. 26 The binary number 1010 representing the decimal number ten = 2 + 8. Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

27. 27 Binary representation of the 1010 the decimal number one thousand ten = 2 + 16 + 32 + 64 + 128 + 256 + 512 Copyright © 2006 Pearson Addison-Wesley. All rights reserved.

28. 28 Technical  At some points, people need to deal in a convenient manner with the way machines are representing information Machines are representing it in a binary form Using just zeros and ones is not handy for us. The base-10 number systems is not efficient for machines.

29. Discrete / Continuous Representations Of numbers – binary & decimal Bits Hexadecimal - 'Hex' Representing text Bits and Bytes Contents

30. 30 Hexadecimal – 'hex'  Base 16 Relatively easy for computers Comparatively easy for us (to read, write, remember, use) Symbols: 0 1 2 3 4 5 6 7 8 9 a b c d e f e stands for fourteen f stands for fifteen 10 stands for sixteen ff stands for two hundred fifty five You've seen this with colours in CSS

31. Discrete / Continuous Representations Of numbers – binary & decimal Bits Hexadecimal - 'Hex' Representing text Bits and Bytes

32. 32 The minimum for representing English and numbers  Lower-case letters  Upper-case letters  Some punctuation  Blank spaces  Frequent symbols

33. 33 ASCII  American Standard Code for Information Interchange  ASCII was 7 bits – an eighth bit was used for various purposes  it became clear that was not enough bits  “Extended” ASCII with 8 bits was developed  Eight bits produce 256 symbols which is more than enough for English and for many European languages

34. 34 ASCII Representing 128 different elements

35. 35 Representation

36. 36 Representation Demo!

37. 37 Bytes & Unicode  IBM gave the 8-bit sequences a special name, byte, and adopted it as a standard unit for computer memory.  Bytes are still the standard unit or memory  The ultimate and complete solution is the representation, called Unicode. It has 8, 16 and 32 bit versions.  It can handle all languages.

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39. 39 Displaying Unicode on PCs In PowerPoint or word or … from the menubar Insert > Symbol > Select Arial Unicode MS Select Unicode Hex Demo!

40. 40 What we need for a global internet  The symbols of all written languages  The symbols of basic and useful symbol systems –Math symbols –IPA "the international phonetic alphabet" Enough space left over to grow € (new symbols get added)

41. 41 And we need these all together  Documents may need to have many languages  What about for example an on-line dictionary (Arabic – Japanese) or …  In addition, a developer would want to be able to build something that would work regardless of the combination of languages needed.  So a unified method of representing all of these together is needed and it is Unicode

42. 42 Encoding  You've seen (and written or copied to heads of html documents): Another example of this would be: Relating it back to HTML etc. The character set for this document is the Unicode Transformation Format – 8 bit

43. 43 Encoding Relating it back to HTML etc. charset means character set iso-8859-1 iso = “ International Standards Organisation ”

44. 44 Symbols & representations Arabic numerals represent numbers Logos represent companies ə ð ɵ represent sounds √ ℵ ∀ ∃ ∂ ∮ ∈ are used in mathematics ¥ ¢ ₨ represent currencies or … ß á â ã ä å À Á Â Ã Ä Å are used in European languages ¶

45. 45 Some representations are better than others  Easier to learn  Easier to remember, easier to store  Easier to process –Roman numerals v arabic numerals  More reliable to communicate  More secure  More accurate  More precise  More flexible What's easy for people What's easy for machines 

46. 46 What is a number again? Using numbers as representations  Phone numbers  License plate numbers  ISBN numbers  National Health insurance numbers We call these ‘numbers’, We use numerals as their representation, but  We don't add them (or...)  They don't have an order (my telephone number is lower than yours)

47. What does ІІ represent? It depends on the context There are at least four reasonable numerical answers that are not just random choices of meaning for ‘I’

48. 48 Explore on your own  In your textbook, there’s a nice explanation of why ‘bytes’. Have a look. – (Chapter 8 of Snyder Fluency with Information Technology)

49. 49 Explore on your own  http://www.unicode.org/ http://www.unicode.org/  http://en.wikipedia.org/wiki/Unicode http://en.wikipedia.org/wiki/Unicode  http://en.wikipedia.org/wiki/Unicode_and_HTML http://en.wikipedia.org/wiki/Unicode_and_HTML  http://www.columbia.edu/kermit/utf8.html http://www.columbia.edu/kermit/utf8.html  Code charts: http://www.unicode.org/charts/http://www.unicode.org/charts/  The absolute minimum every software developer must know […] about Unicode and character sets http://www.joelonsoftware.com/articles/Unicode.html  Unicode's site http://www.unicode.org/standard/WhatIsUnicode.html http://www.unicode.org/standard/WhatIsUnicode.html  On the goodness of unicode http://www.tbray.org/ongoing/When/200x/2003/04/06/Unicode http://www.tbray.org/ongoing/When/200x/2003/04/06/Unicode

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