IT SystemsWhat Number? EN230-1

Justin Champion

C208 – 3273www.staffs.ac.uk/personel/engineering_and_technology/jjc1

IT Systems

Contents What different number systems are there Why do we have them Conversion between

IT Systems We usually use the decimal system to represent

numbers 0,1,2,3,4,5,6,7,8,9 Commonly referred to as Base 10

Machines as seen previously work on the basis of on or off These numbers are represented by 1 or 0

• Commonly known as Binary or Base 2• This binary can be used to represent any of the decimal numbers

IT Systems Each bit in a binary number has a decimal value

Below is a table for a 8-bit binary number

Dec 128 64 32 16 8 4 2 1

Bin 1 1 1 1 1 1 1 1

27 26 25 24 23 22 21 20

IT Systems There can be any number of bits/switches Each of those bits would be a switch

0 = off 1 = on

20212223

1248

IT Systems Each of the bits with are on (1) are added together

This example is Value = 8 + 1 Value = 9

20212223

1248

IT Systems Another example

What is this Value Value = 128 + 64 + 16 + 8 +1 Value = 217

20212223

1248

24

16

25

32

26

64

27

128

IT Systems Significant Bits

Most significant bit• This indicates if there was a change in the binary which part of the

number would have the most effect. Least significant bit

• This indicates if there was a change in the binary which part of the number would have the least effect.

Usually• The most significant bit is the one furthest to the left• Least significant bit is the one furthest to the right

Changes• This is however not the always the case and knowledge of the hardware

and software being used is required• Using encryption is an example where this may change

000000000101010

Most significant bit Least significant bit

IT Systems Significant Bits Conitnued

Another term which is used for this is• Big Endian

• The part of the sequence which has the most effect

• Little Endian• The part of the sequence which has the least effect

000000000101010

Big Endian Little Endian

IT Systems Another example

What is this value? Value = 1099511627775

1111111111111111111111111111111111111111

Take your time working it out !!!!!

IT Systems Why did it take so long to work out ???

There was too many digits you for you to work out The computer would have no problems at all with this

Different number systems We use different number systems to keep it easier to understand for us

Hexadecimal This number system is based upon base 16

Pub quiz question The term hexidecimal comes from the words Greek work Hexa meaning 6 Latin word Decimal meaning 10

IT Systems Hexadecimal lookup table

0 - 16

Hex Dec Hex Dec0 0 8 8

1 1 9 9

2 2 A 10

3 3 B 11

4 4 C 12

5 5 D 13

6 6 E 14

7 7 F 15

IT Systems Hexadecimal

Examples• Decimal 16 = Hex F• Decimal 11 = Hex B• Decimal 27 = Hex 1B• Decimal 64 = Hex 40

Dec Binary Hex0 00000000 01 00000001 12 00000010 23 00000011 34 00000100 45 00000101 56 00000110 67 00000111 78 00001000 89 00001001 910 00001010 A11 00001011 B12 00001100 C13 00001101 D14 00001110 E15 00001111 F

IT Systems Converting between types quickly

Use a calculator ! Ruling that out

Binary to Hexadecimal Break each part into 4 bits If you do not have multiples of 4 then add zeros at the

beginning Calculate each part using the lookup table Put the Hex characters together You have the answer

IT Systems Worked Example

Try this yourself with 11000011

00100110 in Hex

Binary 0010 0110 Hex 2 6

Answer = 26 Hex

IT Systems Usually a symbol is used to indicate what number

types is used Not a problems with binary, but with the others maybe a

problem Hex is usually done by 34f2h

• A h at the end of the number• A $ is used in the programming to indicate hex

IT Systems Conversion between Hex and Decimal

2F.4A to Decimal

(2 * 161) + (15 * 160) + (4 * 16-1) + (10 * 16-2) = 47.74

IT Systems Character representation

We have covered numbers One of the main uses of computers is the movement of

text A standard format is used for text characters called ASCII ASCII = American Standard Code for Information

Interchange This allows for the transfer of characters between

computers and both understanding what was sent.• Issues are common between sending characters between

different operating systems, Panther (Apple), Unix and Windows

IT Systems ASCII

Represented by a 7 bit binary value

H E L L O T H E R E !72 69 76 76 79 32 84 72 69 82 69 33

IT Systems UNICODE

Although ASCII is a worldwide standard UNICODE is a new standard Uses 8bits to represent the characters Supports a larger number of character sets

• Currently supports 34,168 characters Still being expanded Used in the new (Win2000 and above) windows operating

systems. May become popular in the future if other OS’s accept

the standard.• Not that widely used at the moment

IT Systems Summary of what we have discussed

Decimal Binary Hexadecimal Conversion ASCII