Lecture 4 Notes: Bits and bytes Computer Literacy 1 Tuesday 28/9/2004 Lecture Overview Lecture topics: How computers encode information • • How to quantify information and memory How to represent and communicate binary data • The aim is to be able to: Recognise the significance of numbers such as in 256 MB RAM, 32 bit • word length, set of 256 characters etc. Reason quantitatively about computer systems, e.g. Assess the capability • of a system to handle a file of a given size. Computers are digital Computers are built of electric switches: each switch is “on” or “off” at any time. This means that computers process discrete electrical events: they are digital . In contrast, analogue devices process continuous signals. Digital and analogue examples: On an analogue watch the clock hands move continuously, and the time • can be read with an arbitrary level of precision (depending on your eyesight and reactions!) including fractions of seconds. Time increases continuously , as read by the analogue watch. On a digital watch that displays the hours, minutes and seconds, the time • increases in steps of one second. Between seconds, there is no way of measuring what fraction of a second has passed. Time increases in discrete steps , as read by the digital watch. • Modems convert the digital signals in the computer into an analogue signal. This can be sent down telephone wires as an electromagnetic wave. At a receiving computer, the modem converts the analogue signal back into a digital form. Advantages of digital over analogue processing: It is fast . It is much quicker to decide if a switch is “on” or “off” than to • decide how much it is “on” or “off”. It is robust to errors : small errors at each switch in the computer are not • propagated. If a digital switch is a little bit “on” when it should be “off”, then the signal coming from it will still be treated as an “off” signal. If an analgogue switch is a little bit “on” when it should be “off”, then signal will be accepted at the next stage as “a little bit on”. Errors can accumulate this way in analogue devices.
Bits of information A bit is one unit of “information”. Because computers are built out of transistors, which act as binary switches gated by a third input, the smallest level of information that it makes sense to think about is the binary choice. The term bit first occurs in print in 1948, and is attributed to a scientist called John Tukey. It comes from bi nary digi t (~1948). Tukey considered “bigit” and “binit” as possibilities. What a missed opportunity. Each bit has one of two values e.g. 1 or 0. • • Could be represented by Yes or No, True or False, American Idol™ finalists Fantasia or Diana, indeed any binary scheme. Bytes Byte is short for binary term, and was coined in 1956. The mutation from bite to byte occurred around 1956. So the word is a bit weird. • 1 Byte = 8 bits. Originally, the term byte referred to the smallest unit of memory that can be accessed by the CPU. There were computers where this was 6-, 7-, 9-bits. In modern machines, 8-bits has become the standard and the other byte sizes have become obsolete. So 1 byte = 8 bits ! One byte can express 256 (28 ) possibilities. • Each bit has can have one of two values, so for 2 bits, there are 2x2 • possibilities (00, 01, 10, 11). With three bits there are 2x2x2 possibilities (000, 001, 010, 011 and 100, 101, 110, 111). With 8 bits there are 2x2x2x2x2x2x2x2 possiblities, more conveniently written as 28 possibilities The importance of Bytes 1 byte is the minimum unit of memory that can be accessed. Word length of a processor: number of bits a CPU can process at one time: Pentium – 32 bits, 4 bytes Itanium – 64 bits, 8 bytes An example of bytes in use is an internet “IP” address e.g. 129.215.155.141 (IP addresses will be explain in later lectures) Big Bytes 210 bytes = 1024 bytes ~1000 bytes 210 bytes = 1 kilobyte = 1KB So 1 KB is not 1000 bytes (N.b. 22 = 2x2, 23 = 2x2x2, 25 = 2x2x2x2x2 etc) 1 Megabyte (MB) = 1,048,576 bytes = 220 bytes = 1024 KB ~109 bytes 1 Gigabyte (GB) = 1,073,741,824 bytes = 230 bytes = 10242 KB ~109 bytes 1 Terabyte (TB) = 240 bytes = 10243 KB ~1012 bytes 1 Petabyte (PB) = 250 bytes = 10244 KB ~ 1015 bytes Then exabyte, zettabyte and yottabyte! Maybe in your lifetime!
How big is big? Develop a sense of how big files are and you will do yourself a big favour, avoiding opening huge files with innapropriate applications, knowing when you have generated files of junk etc. You will also be better able to assess the capability of a system. 300 page novel 0.5 MB Floppy Disk 1.44 MB 3 minute MP3 track 2 MB Edinburgh telephone directory 20 Mb CD-ROM 600-700 MB DVD 4 GB Corporate customer database 1 TB Video of your life 1 PB Human brain > 10 PB Hexadecimal (Hex) Binary arithmetic is counting in 2s. Normally we count in 10s. Hexadecimal arithmetic is counting in 16s. Bits can be expressed in hexadecimal without losing any information. • • It is easier for humans to read! • Because bytes can be expressed using two numbers in hexadecimal (one hex digit for the first 4 bits, and one hex digit for the next 4 bits), it is a very widely used system for expressing binary code. You won' t have to do hex arithmetic in the exam. You should be able to recognise it though. Counting in different bases In normal (base 10) counting, 1101 = 1 x1000 + 1 x100 + 0 x10 + 1 x1 = 1 x103 + 1 x102 + 0 x101 + 1 x100 So each position quantifies a power of 10. when you count in a different “base”, each digit quantifies a power of the base number you are counting in. Because computers process binary bits, computer talk requires talking about numbers in terms of base numbers which are multiples of 2. Below are some examples of counting in relevant bases: In base 2, 1101 = 1 x23 + 1 x22 + 0 x21 + 1 x20 = 13 (base 10) In base 8 (octal) 1101 = 1 x83 + 1 x82 + 0 x81 + 1 x80 = 83 (base 10) In base 16 (hex) 1101 = 1 x163 + 1 x162 + 0 x161 + 1 x160 = 4368 (base 10) Counting in Hex The sixteen digits of Hex are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F When you get to the number for ten, if you used “10” it would be • interpreted in hex as one unit of sixteen plus zero ones (as the counting in different bases examples above show). Creating new digits to express the
numbers from ten to fifteen is therefore a lot less confusing. The original choice of using letters to do this job was arbitrary, but this is the convention. Now keep counting! 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F So 1A (base 16) = 1 x16 + 10 x1 (base 10) = 26 (base 10) and 1B (base 16) = 1 x16 + 11 x1 (base 10) = 27 (base 10). • Hex is normally written using “#” or “0x” to indicate the number is in hex form. E.g. #AB3 or 0xAB3 means AB3 (hex), AB3 (base 16), AB3 16 You will come across hex in many occaisions if you work with computers. • To know about hex is to be enabled in the computer world. • One example of hex in practice is the “non-dithering RGB colour codes”. “Dithering colours” are colours which look different on different web browsers, and a common fault of many websites. Colours defined by their red green blue (RGB) code, which specifies how much red, green and blue is in the colour, look the same using every web browser. The “non-dithering RGB colour codes” are binary codes, expressed in hex. • The above are examples of non-dithering RGB colours and their hex codes (printed in greyscale). Each code is three bytes long, and each byte is expressed using two numbers in hex. So the code #CC3399 expresses one byte of information about the level of red (#CC), one byte of information about the level of green (#33) and one byte about the level of blue (#99). Easy, see! Expressing characters Computers process bits of information, but we process language through characters. There are standard conventions that define how characters are expressed in bits. The standard conventions include: • ASCII, Unicode, ANSI, ISO Latin ASCII is a very common convention used in many situations. Its weird name stands for American Standard Code for Information • Interchange (don' t learn this! It' s just to make the acronym less mysterious). The convention works as a dictionary, allowing keystroke characters to be translated into binary form.
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