[PPT] - 3. Back to fundamentals Bits, bytes and all that CL1 2003/4-3 1 PowerPoint Presentation

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3. Back to fundamentals

Bits, bytes and all that

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Once upon a time …

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Analogue and Digital

Modern computers are digital computers
Given a quantity (e.g. voltage somewhere)

– Decide if there’s a voltage (1) or no voltage (0)

Fast; lots of very simple decisions made very quickly
Easy to transmit - degradation has to be extreme before you get

error

Alternative were analogue computers

– Very restricted; utterly unlike digital computers – Analogue computation lurks in the sidelines

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The binary bit (see handout)

The basic unit handled by all processes in a

digital computer is the binary bit.

It may take the value 0 or 1.
3 bits: 000, 001, 010, 011, 100, 101, 110, 111

– 8 (23) possibilities. Represent numbers 0 - 7 – ... Or numbers –4 to +3, or 0 to 1 in steps of 1/8 – … or North, North-East, East, … – … red, green, blue, cyan, yellow, magenta, black, white … etc. etc. – any collection of 8 things.

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Collections of bits - 1

8 bits together can represent 256 (28) possible values:

– Numbers 0 to 255; (or –128 to +127); or a character. – A group of 8 bits is called a byte or an octet

10 bits together can hold 210 or 1024 possible values;

1024 is close to 1000 and ‘K’ in computer terminology usually means 1024 rather than 1000.

Powers of 2 are ‘round’ numbers in computing terms
Binary numbers are unwieldy (200310 =

111110100112) and are usually represented in octal (base 8) or hexadecimal (base 16) notation.

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Base N examples

In normal (base 10) arithmetic, 1234 stands for…

1 * 1000 + 2 * 100 + 3 * 10 + 4 * 1

i.e..

= 1 * 103 + 2 * 102 + 3 * 101 + 4 * 100

In Base 2, 1101 means

1 * 23 + 1 * 22 + 0 * 21 + 1 * 20 (= thirteen)

In Base 8 (octal), 123 means

1 * 82 + 2 * 81 + 3 * 80 (= eighty-three)

In Base 16 (hexadecimal), 1D means

1 * 161 + D * 160 (= twenty-nine)

[‘D’ = 13]

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Hexadecimal

Hexadecimal arithmetic is base 16
Digits are 0-9 and A-F
There is a relationship between hexadecimal and

binary = each hex digit represents four binary bits

200310 is 111110100112 which is 111| 1101 | 0011

= 7D3 in hexadecimal

Written 0x7D3, #7D3 etc.
(similarly octal digits each represent 3 binary bits)

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Note …

You will not be asked to do hex or octal arithmetic

in an exam but might be asked to ‘count on your fingers’ in binary, hex or octal

Key issue here is to recognise these numbers when

you see them and have some idea of what lies behind them

Why for instance numbers like 32, 64, 255 (256)

are significant

See handout for more background

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Collections of bits - 2

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The maximum number of bits a processor can

handle in a single operation is called the word length and in modern machines is typically 32 or 64.

2word length - 1 is the largest (unsigned) integer the

computer can conveniently store exactly.

The power of a processor depends on the raw

processor speed and the word length among other things.

The speed of a computer system depends on many
ther factors as well.

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Examples

GENERAL PROTECTION FAULT, addr = 2FEF

3C00 [“Blue Screen of Death”; hex address of where error occurred].

<body bgcolor=“#F0F0C0”> [hex number

describing amounts of Red, Green and Blue (RGB) in a Web page colour, range 0-255]

129.215.128.57 [Internet ‘IP’ address; each

number will be between 0 and 255]

Computer ‘MAC’ address: 00-C0-86-4A-07-F6

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Units of measure

1 byte

1

20 100 1 Kilobyte Kb 1 Thousand 210 220 230 240 250 ~103 1 Megabyte Mb 1 Million ~106 1 Gigabyte Gb 1 Billion (US) ~109 1 Terabyte Tb 1,000 Billion ~1012 1 Petabyte Pb 1,000,000 Billion ~1015

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A few sample data sets

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300 page novel 0.5 Mb screen capture of a PC screen at high resolution 2.3 Mb 3 minute sound track recorded as MP3 2 Mb 30 second video clip at low resolution 2 Mb Edinburgh telephone directory 20 Mb Typing 4 characters/second, 8 hrs/day for a year 42 Mb Corporate Customer database, e-Science n Tb Library of Congress 100 Tb Video of your entire life 1 Pb Human brain, big e-science n Pb

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Size limits

A computer needs to be able to index each

separate byte in memory or a file (e.g. byte 123 in file ‘fred’).

The limits on memory and file sizes (also disk

blocks) will be binary ‘round numbers’.

This is why you may find memory on a PC is

limited to 4Gb or hard disks on old PCs are limited to 2Gb etc. etc.

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Characters are coded

One per byte, ASCII encoding:
A

0x41 (0)100 0001

B

0x42 (0)100 0010

C

0x43 (1)100 0011

c

0x63 (0)110 0011 (lower-case)

Ctrl-A

0x01 (1)000 0001

Can only represent 128 characters this way
8th bit is reserved for error detection - parity
Even parity even number of ‘1’s in code

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Some characters don’t travel well

ASCII

7 bits+1 128 values

€, ¥, §, à, é, ç as coded need 8 bits
Alternatives:
Latin 1(extended ASCII) 8 bits

256 values

Unicode

16 bits 65536 values

But then …
“$” “local currency symbol” (£,$, …) etc.

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Email character quoting

I went to see “Une Femme Française” at the
Filmhouse. Tickets were £6.50

Becomes

I went to see =B4=B4Une Femme

Fran=E7aise=B4=B4 at the Filmhouse. Tickets were =A36.50. Or..

<html><body>I went to see “Une Femme

Fran{aise” at the Filmhouse. Tickets were £6.50.</html></body>

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Encoding Binary files

Need general mechanism for sending

programs, images etc. as text mail attachments

– 1. Method of encoding binary file – 2. Some means of telling far end what it is

Multimedia Internet Mail Extension (MIME)

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Your frog is in the mail …

CL1 2003/4-3 19 From: "John Butler" <jhb@ed.ac.uk> To: <asw@dcs.ed.ac.uk> Subject: frog Date: Mon, 01 Oct 2002 11:45:36 +0100 date, timezone MIME-Version: 1.0 Content-Type: image/gif; file type name=“FROG.GIF" Content-Transfer-Encoding: base64 file encoding Content-Disposition: attachment; filename=“FROG.GIF" R0lGODdhgwBwAPcAAP///97W1s7Gxntzc+/e3pyMjJSEhMalpYxzc7WUlKWEhJxzc3taWiEYGBAI CBgICGsYGGsICL0YEM4YELUQCL0QCJwYELUYEIwQCJwQCLVaUnMQCKWlpZRCObUpGFIQCMaUjL2E e4xSSrVCMaUpGM5rWoQhEM6Ec61jUsYxEGtKQlo5MTEQCLU5GNY5EHtCMa1aQq1SOaU5GNZzUmMx Ib1aOXsxGOeljLVzWoxKMc5KGJRrWueEWkohEMZKGM69tWtaUt6Uc1IxISkYEJxSMc7OzrWEa2NC MYRSOc5rOdZaGLWlnM6Uc85aGK2UhM6ce4xjSrVzSrVaIZyEc4RrWs6EUueUWrVrOcZjIdZrIc6t lJRzWu+te7WEWuela5xrQsZ7OdZ7MZxaIcZrIca9tYR7c0IxIb1rIb21rbWtpVpSSufGpdathHtj Sr2Ua96te86UWhgQCEoxGNaMQt6MOdZ7IWtjWue9jOe1e86cY8aUWoRSGLWUa4xjMc6MObV7MdaM Ma2chOe1c96ta9alY6V7Qr2MSs6EIYRzWq2MWt6lUs6MKd6UKda9lO+9a86cSr2MOeelOZyEWt61 a97OrfferefOnOfGhM6ta2tSIc6cOZxzIbWEIe/n1rWtnJSMe4yEc1JKOda9hO/OhN61WtalOc6c … etc. … encoded file

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Base64 Binary file encoding

Take 3 bytes of the file (3 * 8 = 24 bits)
Encode as 4 * 6-bit characters (4 * 6 = 24); add ‘0’
Repeat.
File increases in size by 25% but doesn’t get mangled

en route

MIME-type lets receiving mail process know what sort
f file it is
Alternatives: uuencode (Unix), binhex (Mac)

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Key Points

Computers manipulate bits (0,1) very quickly
Binary numbers are unwieldy, use hex or
ctal instead – understand counting in hex etc.
Characters encoded as ASCII
Need some encoding to send non-text

information over email, e.g. MIME-encoding

Recoginse encoding when you see it