LIS512 lecture 3 numbers and characters

1. Thomas Krichel 2010 – 10 – 06 LIS512 lecture 3numbers and characters

2. structure • numbers • numeric information • character information • the ASCII set • Unicode • encoding • coda • ligatures • collations • transliterations

3. introduction • We have seen that databases store records. • Records contain fields, fields have values. • Here we talk about fundamentally, how do we compose those values. • Numeric values are easy. • Character values are harder.

4. literature • The library textbooks are hopelessly short and confused about this topic. • I have most of what I have here from my own experience. • I recommend Wikipedia, it has fascinating articles about these topics.

5. all gone to a number • In all modern information system, information is stored to be treated on a computer. • A computer can only deal with numbers. • As a consequence all information has to be converted into a number. • It's a huge job. • Let’s look at the ground, numbers.

6. binary code • All computers process codes that is a sequence or zeros and ones. • Such code is called binary. • All digital information is somewhere written out as sequences of on/off binary signals.

7. binary and digital numbers • Binary numbers can be converted to normal “decimal” numbers • 0 0 • 1 1 • 10 2 • 11 3 • 100 4 • 101 5 • etc

8. a bit • A bit is the elementary unit of information. • It takes a binary value. We can label it true/false, black/white, +/-, etc. • Every piece of information in all modern information storage systems has to be reduced to a sequence of bits. • We will denote them 0/1 here.

9. example: 2 bits • If we say that an piece of data is three bits long, we know it can hold 2 to the power 2 different numbers. • In binary, they are 00, 01, 10, 11. • In decimal, they are 0, 1, 2, 3.

10. byte • A byte is a sequence of 8 bits. '00000000' to '11111111'. There are 2 to the power 8, meaning 256 possibilities to write a byte. • If the byte is required to start with 0, then we can only write '0000000' to '01111111'. This leaves us with 2 to the power 7, meaning 128 possibilities.

11. hex numbers • Hex numbers contain the usual digits 0 to 9, as well as A to F. A means 10, B means 11, etc F means 15. • One hex number can represent 2 to the power 4, meaning 16 possibilities (0 to 15). • Two hex numbers can represent 2 to the power 8 possibilities.

12. one hex number 0 0000| 10001 2 0010| 3 0011 4 0100| 5 0101 6 0110| 7 0111 8 1000 | 9 1001 a 1010 | b 1011 c 1100 | d 1101 e 1110 | f 1111

13. same in decimal number 0 0000 | 1 0001 2 0010 | 3 0011 4 0100 | 5 0101 6 0110 | 7 0111 8 1000 | 9 1001 10 1010 | 11 1011 12 1100 | 13 1101 14 1110 | 15 1111

14. bytes and hex numbers • Since two hex numbers convene the same number of possibilities as a byte a byte is often represented as two hex numbers. • Thus, for example • '00000000' in binary is 00 in hex, • '11111111' in binary is 'FF' in hex, • '01111111' in binary is ‘7F‘ in hex

15. another way to see this… • binary numbers are sometimes called base-2 numbers. • decimal number are sometimes called base-10 numbers. • so hexadecimal (hex) numbers are just base-16 numbers. • sometimes written using a 0x prefix.

16. converting information to numbers • A lot of problem in converting information comes from some part of the information encode in some form and some other part in some other from. • Example: “15 Julliet 1923” vs “July 17, 1923” • Often such inconsistencies require manual reformatting, which is very expensive.

17. numerizing • In the design of every information systems, if possible it is a good idea to convert information into something that is directly a number. • There are examples where it is possible directly use a number, such as • colours • times and dates • locations.

18. example: colours on the web • Colours on the world wide web follow the red/green/blue colour model. • Each colour is given as a number #rrggbb, where rr is the amount of red ggis the amount of green and bb in the amount of blue. All these numbers are hex numbers. Example • #FFFFFF white • #00FFFF aqua

19. example: times • One way to “numerize” recent times in to take the number of seconds since the first of January 1970. • This point in time is called the Unix epoch. • Counting time like this has the advantage that it is straightforward to interpret and to convert it into a representation of time that the user can understand.

20. example: location • On earth, locations are best given by a longitude / latitude grid system. • This for example, makes a rough calculation possible on how far two points are apart. • It also allows us to refer to a location independently of its current name. Remember, names of locations change.

21. non-numerical information • A lot of information is not numerical by its nature. For example • the name of a person • the title of an expression of a work • The information is of a character string nature. • To store character strings in an information system, each character has to be converted to a number.

22. character • A character is an indivisible unit of textual information. • Textual information is composed of characters, and nothing else.

23. characters and computer • Computers can not deal with characters directly. They can only deal with numbers. • There we need to associate a number with every character that we want to use in an information encoding system. • A character set combines characters with number.

24. ASCII • ASCII is an old character set developed in the United States. It is a seven bit character set. • In hex notation, it goes from '00' to '7F' • Because Anglo-Saxon cultural imperialism, most other character set either include or extend the ASCII character set.

25. notable characters in ASCII decimal hex byte • 8 8 08 U+0008 backspace • 9 9 09 U+0009 horizontal tab • 10 A 0A U+000A line feed • 13 D 0D U+000D carriage return • 32 20 20 U+0020 space • 127 7F 7F U+007F delete

26. UCS / Unicode • UCS is a universal character set. • It is maintained by the International Standards Organization. • Unicode is an industry standard for characters. It is better documented than UCS. • For what we discuss here, UCS and Unicode are the same.

27. Basic multilingual plane • This is a name for the first 65536 characters in Unicode. • Each of these characters fits into two bytes and is conveniently represented by four hex numbers. • Even for these characters, there are numerous complications associated with them.

28. wikipedia notation • Wikipedia denotes every character in the BMP as U+hhhh where h is a hex digit 0-F. • We will follow this notation here. • This notation is also useful when you try to enter the characters on a computer. • For example, in MS Windows, you • press and hold ALT • press + on the numeric keypad • enter the hex code • release ALT

29. ascii and unicode • The first 128 characters of UCS/Unicode are the same as the ones used by ASCII. • So you can think of UCS/Unicode as an extension of ASCII.

30. dashes • figure dash ‒ U+2012 to link numbers without a range • en dash – U+2013 to link numbers with a range • em dash — U+2014 for interjections in a sentence • minus sign − U+2212 for mathematics

31. “smart” quotes • U+201c “ is the opening double quote • U+201d ” is the closing • U+2019 ’ is the apostrophe • The single quote of the ASCII character set is considered to be of mixed usage, it should be avoided when a specific use can be done. • Similarly, the double quote of the ASCII character set is imprecise.

32. spaces • non-breaking space, U+00A0 is used when you want to avoid a line break between the two spaced items. For example in hyperlink text, it is good practice to replace spaces with non-breaking spaces as to avoid there appearing to be two links. • In whitespace collapsing contents, it can also be use to add extra space.

33. in foreign languages • Everything becomes difficult. • As an example consider the characters • o • ő • ö • The latter two can be considered o with diarcitics or as separate characters.

34. most problematic: encoding • One issue is how to map characters to numbers. • This is complicated for languages other than English. • But assume UCS/Unicode has solved this. • But this is not the main problem that we have when working with non-ASCII character data.

35. encoding • The encoding determines how the numbers of each character should be put into bytes. • If you have a character set that is has one byte for each character, you have no encoding issue. • But then you are limited to 256 characters in your character set.

36. fixed-length encoding • If you have a fixed length encoding, all characters take the same number of bytes. • Say for the basic-multilingual plane of unicode, you need two bytes for each character, and then you are limited to that. • If you are writing only ASCII, it appears a waste.

37. variable length encoding • The most widely used scheme to encode Unicode is a variable length scheme, called UTF-8. • It is important to understand that the encoding needs to known and correct.

38. bascis of UTF-8 • Every ASCII character, represented as a byte, starts with a zero. • Characters that are beyond ASCII require two or three bytes to be complete. • The first byte will tell you how many bytes are coming to make the character complete.

39. byte shapes in UTF-8 encoding • 0?????? ASCII • 110???? first octet of two-byte character • 1110???? first byte of three-bytecharacter • 11110??? first octet of four-byte character • 10??????? byte that is not the first byte • as you can see, there are sequences of bytes that are not valid

40. hex range to UTF-8 • 0000 to 007F 0??????? • 0080 to 07FF 110????? 10?????? • 0800 to FFFF 1110???? 10?????? 10??????

41. ligature • In fine traditional typography, certain characters appear to be linked to each other. • The most command examples in English usage are fi, ff, fl, ffi, ffl.

42. ligatures growing up • In certain cases, ligatures have become so common that they have become characters of their own. • A prominent example is the German sz ligature the esszet. It looks a bit like a beta because it is derived from the fraktur font of the characters. • Another example, apparently, is &.

43. collations • Collations are topic that is related to characters. • A collation is a sorting order of character strings. • You may think this is trivial, just follow the alphabetic order. • But in many languages, diacritics come to complicate matters.

44. example German • Here are the extra letter of German: Ä/ä, Ö/ö, Ü/ü, ß • In German, there are two collations. • DIN 5007-1 “dictionary collation” treats umlauted characters as if they did not have them, and ß as s. • DIN 5007-2 “phonebook collation” treats umlauted as letter and e (ex. ä --> ae), and ß as ss

45. transliterations • When non-English characters are supposed to be entered in a system used by English speaking people, a transliteration might be used. • This can also be the case if the original script may not be commonly understood. An example are Japanese road sign. • Wikipedia lists 20 different ways to do that for Russian, say. Library of Congress scheme is apparently the most widely used.

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