Symbols and Meaning. Data Representa+on and Encoding. Encoding 1/13/12

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1 Symbols and Meaning Compu+ng and Reasoning Computa+on in the physical world Computa+on as Manipula+ng Symbols Language, mathema+cs and computa+on use symbols to represent concepts and objects Computers manipulate symbols and these manipula+ons mean something Because the symbols mean something In the 1930 s s computer designers began to realize that if they made their computers programmable, they could change what the symbols mean and what the computers did without having to build a new computer for each new problem or applica+on Data Representa+on and Encoding Encoding Computers use binary code (zeros and ones) to record informa+on. Binary digits (bits) can be recorded on different storage media electrically, (on a chip) magne+cally (on a hard drive or magne+c tape) or op+cally (on a DVD). Holes in paper (tape and cards) were once used for data storage. Since all data in all files are reduced to binary codes for recording and storage, any type of file can be recorded on any storage media. The difference is how the informa+on is encoded in binary. You can use any symbols you want, but they are encoded in binary codes to be stored or manipulated by computers. For example, one binary code for text informa+on is the ASCII code. (UTF, ANSI are other text code varia+ons). Other binary codes are used for other types of data INFORMATION ENCODED Images Video JPEG, GIF MPG, AVI UTF, ANSI TO BINARY STORED IN FILES ON STORAGE MEDIA Op+cal Disk/DVD Magne+c Hard Drive Why do computers use binary? It s not inherent in the natural world (that is, we don t have to choose binary) It is technologically simple to have a two state device (1 or 0, on or off) - a switch - to represent in computer circuits (chips) or memory devices Text MP3, WAV Sound USB Key

2 Teletype ASR- 33 input/ output terminal device designed to be compliant with ASCII encoded messages Why do computers use binary? It was adopted by early computers, so this make it easy for new machines and programs to follow the binary schemes already adopted 58 Why do computers use binary? The important observa+on is: no maier what conven+on was chosen (in this case, binary) any symbol system can be encoded or translated into the conven+onal choice It is not necessary to design a new computer for every new language, mathema+cal system or type of computa+on we want to perform; we simple subs+tute or change the encoding and the programs we use 59 An Example of Binary Encoding: ASCII Char Decimal Binary Char Decimal Binary Char Decimal Binary NUL SOH ! A STX " B ETX # C EOT $ D ENQ % E ACK & F BEL G BS ( H TAB ) I LF * J VT K FF , L CR M SO N SI / O DLE P DC Q DC R DC S DC T NAK U SYN V ETB W CAN X EM Y SUB : Z ESC ; [ FS < \ GS = ] RS > ^ US ? _ Char Decimal Binary ` a b c d e f g h I j k l m n o p q r s t u v w x y z { } ~ Δ An example of Binary Encoding: Binary Numbers One hundred fily eight in base 10 (decimal) Numbers can be encoded in binary, using base in the 1 s place (100) 5 in the 10 s place (10 1 ) 1 in the 100 s place (10 2 ) 61 One hundred fily eight in base 2(binary) in the 1 s place (2 0 ) = 0 1 in the 2 s place (2 1 ) = 2 1 in the 4 s place (2 2 ) = 4 1 in the 8 s place (2 3 ) = 8 1 in the 16 s place (2 4 ) = 16 0 in the 32 s place (2 5 ) = 0 0 in the 64 s place (2 6 ) = 0 1 in the 128 s place (2 7 ) = Binary Number Arithme+c one plus one 10 is two 1 with a carry.. 1 one plus one + 1 plus one more 11 is three one hundred fifty eight plus sixty-one is two hundred nineteen

3 Encoding different data types Other informa+on types (images, video, music) must have different binary encodings for the informa+on to be stored in files. Some+mes files can have mul+ple types of encodings within the file format. Such as a web browser, which display images and text. In order to display informa+on properly, each applica+on must use the coding appropriate to the file format. Note the numerals can be encoded for text display or for arithme+c (as numbers). This dis+nc+on is important for programs that display both text and numbers. Data and file types Different types of data are encoded, or represented differently. The type or format of a file will olen reflect the encoding of a par+cular type of data stored in the file, such as audio, images, video, or text. One way the file type can be indicated is by providing a filename extension, which conven+onally is the last part of the name following a dot. Some example are: Extension.mp3.wav.mp4.avi.mov.jpg.gif.+ff.zip.html.htm.xml.vrml.exe.pdf.pptx Data type Audio file formats Video file formats image file formats Compressed zip archive Hypertext and media markup formats used for web page source Program code for executable programs (Windows and some other opera+ng systems) Portable document format (Adobe) Microsol powerpoint File type conven+ons Keep in mind that filename extensions are a conven+on, not a property of the data in the file a file can have the wrong file extension different programs may use the same extension for different formats The file format might be different than the extension indicates Microsol Windows desktop tries to launch an associated applica+on when you open a file. This is based on the file name extension..odt Openoffice text Bits and Bytes: data size Storage and Memory In order to represent different type of data or informa+on, groups of bits are olen needed A group of 8 bits is called a byte. (One bit is not very useful encoding unit for most data). Storage, memory capacity and file size are characterized in bytes: KB kilobytes (1000 s) thousands Range of a typical text file MB megabytes ( s) millions Range of a typical digital photo GB gigabytes ( s) billions Range of typical removable media or computer memory TB terabytes (10 12 ) Range of typical large storage device (hard drive) One peculiarity is that computer specifica+ons have a history of coun+ng in base 2 binary. For example, according to that conven+on, the prefix kilo was used for a count of 2 10, which works out to 1024 instead of the standard metric conven+on of kilo meaning of Main memory sizes, for example, use the binary coun+ng conven+on. If you re used to the metric prefix, it seems like you re gerng a liile bit extra. Don t confuse main memory and storage Memory holds data and programs in ac+ve use by the processing components of the computer Typical hardware for this is vola+le RAM RAM = Random Access Memory Vola+le means power- off blanks the memory and requires a re- boot» Laptops have sleep or hibernate modes to keep the memory from blanking More memory more simultaneously ac+ve programs and tasks Storage records data and program permanently (or un+l deliberately deleted) on some storage memory Organized into files in a file system Some recording media involved and a device that records on that media Media can be removable (like DVDs) or fixed (Hard drive) Programs have to be loaded from storage into main memory to run, and data is usually loaded into memory to be manipulated

4 Levels of encoding We can think of levels of encoding to represent something, using different symbols or representa+ons For example, English text can use symbols that are encoded in UTF/ASCII (one level of encoding), which are internally represented or encoded in binary (a second level of encoding): From the screen.. It was the year of Our Lord one thousand seven hundred and seventy-five. Spiritual revelations were conceded to England at that favoured period, as at this. Mrs. Southcott had recently attained her five-and-twentieth blessed birthday, of whom a prophetic private in the Life Guards had heralded the sublime appearance by announcing that arrangements were made Encoded into UTF- 8 for the swallowing up of London and Westminster Encoded into binary Into physical media (op+cal/magne+c/electronic) Or a computer program as wriien by a programmer in a computer language.. C- Language Encoded into UTF- 8 UTF- 8 as binary From the screen.. #include <stdio.h>! int main(void)! {!!!printf("hello, world\n");!return 0;! }! Stored on physical media (op+cal/magne+c/electronic) Or a web page as browsed by a web user.. From the screen.. Web page on screen Web page represented in HTM language HTML encoded as UTF- 8 binary codes <!DOCTYPE HTML PUBLIC "- //W3C//DTD HTML 4.01 Transi+onal//EN" "hip:// loose.dtd"> <html> <head> <+tle>become an Undergraduate Student Welcome to Memorial</ +tle> <link href="hip:// brand/2011v1/include/styles/base.css" rel="stylesheet" type="text/css" media="screen" /> <link href="hip:// 2011v1/include/styles/structure.css? " rel="stylesheet" type="text/css" media="screen" /> <link! Stored on physical media or transmiied across the internet

5 1/13/12 Other encoding examples.. Other ideas for encoding Images are made up of pixels: each pixel might be encoded as a Red, Green and Blue intensity (100%, 10%, 0%) = The 3 numbers can then be converted to an 8 bit binary value, so each pixel takes 3 bytes to represent In Class Exercise Encode yourself! Encoding exercise hints and choices Propose an encoding for our class sea+ng plan Use convenient symbols Ul+mately, you must come up with (and explain) an encoding scheme that can indicate which student is in which seat Your encoding must (eventually) be in binary You can incorporate an exis+ng code (ASCII, binary numbers) or make up your own You can iden+fy things (seats, students) using your own symbols or strategy You can start using binary directly Or you can have some levels of symbols before you get to binary Or you can use exis+ng iden++es (such as student names?) You have to convert them to binary eventually 78 Another Hint about file structures.. 79 Reviewing the exercise Some things that weren t specified in the problem: Computer files are generally understood to be sequen+al In other words, there is a first symbol in the file, a second symbol in the file, a third thing and so on For example, if this slide were stored in a file, the word Another is first, then the word Hint Leier A comes first, then n, and so on.. The corresponding binary codes are arranged in the appropriate order in the file containing the slide.. So we don t have to encode which thing comes first or second or third; we put them in the computer file in the right order You may be able to use the order of symbols in the file to make your encoding easier But you can ignore this if its more confusing than helpful 80 Does the encoding scheme have to work for any sea+ng arrangement or only our sea+ng arrangement? Does the encoding scheme have to work for all classrooms, or only our classroom? Does the encoding scheme have to work for all possible groups of students or only our group of students? Does the encoding scheme have to indicate if the seats have been moved around to a new loca+on or not? These are ques+ons about the expressive power of the language or encoding scheme you have created, and they echo basic ques+ons about compu+ng (Hilbert) Does computer provide every thing that can be expressed? (Goedel) Are all true things provable with a computer? (Turing) 81 5

6 An alerword Machine Code Simplified computer architecture diagram There is one special code machine code - that is built into the computer processor Machine code is the binary code that indicates which circuits the computer should ac+vate to run a computer program Computer circuits correspond to opera+ons on binary symbols; for example there are circuits for add, subtract, compare, copy, and moving binary values in and out of computer memory and storage. So machine code already has a meaning within the machine those binary code symbols mean the computer circuits to ac+vate. The meaning of each code (what the corresponding circuit does) is referred to as an instruc0on To create a computer program, these codes have to be arranged (or compiled) into the correct sequence to produce the desired result To run a computer program, the processor(s) takes a sequence of machine coded instruc+ons and ac+vates the corresponding circuits in sequence order. When they re not being used, the coded program instruc+ons (which as a whole comprise a program) are kept in a file on a storage medium (such as a hard drive or usb key), just like any other informa+on on the computer. Computer Architecture refers to the organiza+on of hardware (the physical parts) of the computer Electronic circuits on computer boards and chips include these components: The processor contains the circuits ac+vated by machine code Memory stores the data (including the machine code) currently in use by a running program Controllers are circuits that control computer devices (such as screens, hard drives, usb keys, wireless receivers) according to the binary codes that are sent to them. Each controller is designed to control par+cular devices according to its own codes. A bus is a pathway of wires for sending binary coded signals among components (for example, from a storage controller to memory). A storage device contains data (and programs) organizing into files and recorded on a storage media. A tradi+onal name for storage is Secondary Memory. Processor Memory Controller Controller Controller BUS Controller Storage Storage Programmers don t write in machine code (anymore) Binary machine code is good for designing machines that run programs, not so good for human programmers to understand Instead, humans write programs in formalized programming languages (like C or Java), and a program translator translates them into machine code Programming languages are a kind of middle ground: easier to read and write than machine code (for humans), and easier to translate into machine code than English (for computers) Don t confuse encoding (represen+ng concepts or symbols using coding symbols) with transla0on (changing from one encoding to another encoding). In the computer world, these are different ideas. 84 Program transla+on is not encoding #include <stdio.h>! int main(void)! {!!!printf("hello, world \n");! return 0;! }! Source program: in this example, C- Language code is one thing stored in one file, which can be viewed in different ways, including its binary representa+on Program transla+on Machine- Language program: this is a different thing which can be stored in a different file. It it the transla+on of the program that can be run on a 85 computer as a program. Final thoughts on symbols and encoding.. Concepts are represented by symbols Computa+on is performed by manipula+on of the symbols We have to decide what the symbols mean There is a sense in which it doesn t maier what symbols you use Because we can always encode using other symbols As long as we are careful about the encoding Computers use binary, but we can encode whatever we want into binary using our own code What you decide the symbols represent (that is, their meaning) does maier a great deal It might determine what is possible or impossible to compute (or, in scien+fic terms, to model) 86 6