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Section 1: Data Representation NS

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Section 1: Data Representation NS

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1.1 Number Systems

Created by

Jonathan Dunsby
Jonathan Dunsby
Singapore

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Section 1: Data Representation NS
 

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Section 1: Data Representation NSOnline version

1.1 Number Systems

by Jonathan Dunsby
1

No matter how the system , the basic building block in all computers is the number system . This system is chosen because it only
consists of and 0s . Since computers contain millions and millions of tiny ? switches ? , which must be in the ON or position , they can be represented by the binary system .

2

A switch in the position is represented by 1 ; a switch in the OFF position is represented by . Switches used in a computer make use of gates and are used to and process data .

3

The binary system
We are all familiar with the number system which counts in multiples of . This gives us the well - known headings of units , 10s , 100s , 1000s , and so on : Denary uses ten digits , 0 - , to represent all values . Denary is known as a 10 number system .
The binary number system is a base number system . It is based on the number 2 . Therefore only the two ? values ? 0 and 1 can be used in this system to represent all values .

4

The conversion from binary to is a relatively straightforward process . Each time a 1 - appears in a number column , the column value ( heading ) is to a total .

5

The hexadecimal number system is very closely related to the system . Hexadecimal ( sometimes referred to as simply ? hex ? ) is a 16 system and therefore needs to use different ? digits ? to represent each .

6

As Hexadecimal is a system based on different , the numbers to 9 and the letters A to are used to represent each hexadecimal ( hex ) digit . A in hex = in denary , B = 11 , C = 12 , D = 13 , E = 14 and F = 15 .

7

Since Hexadecimal uses 16 : = 2 TO POWER OF , this means that FOUR binary are equivalent to each digit .

8

Converting from binary to is a fairly easy process . Starting from the and moving left , split the number into groups of 4 . If the last group has less than bits , then simply fill in with 0s from the .

9

A computer can only work with data . Whilst computer scientists can work with binary , they find hexadecimal to be more convenient
to use . This is because one hex represents binary digits . A complex number , such as 1101001010101111 can be written in hex as D2AF . The hex number is far easier for humans to remember , copy and work with .

10

Error are often shown as values . These numbers refer to the location of the error and are usually automatically generated by the computer . The programmer needs to know how to the hexadecimal error codes .

11

Media Control ( MAC ) address refers to a which identifies a device on a . The MAC address refers to the network card ( NIC ) which is part of the device .

12

Each device connected to a network is given an address known as the Internet ( IP ) address . An IPv4 address is a 32 - number written in or hexadecimal form : e . g . 109 . 108 . 158 . 1 ( or 77 . 76 . 9e . 01 in hex ) . IPv4 has recently been upon by the adoption of IPv6 . An IPv6 address is a - bit number broken down into 16 - bit chunks , represented by a number .

13

HyperText Mark - up ( HTML ) is used when writing and developing web pages . HTML isn ? t a language but is simply a mark - up language . A mark - up language is used in the processing , definition and of text ( for example , specifying the colour of the text ) . HTML is often used to represent of text on the computer screen . All colours can be made up of different of the three primary colours
( red , green and blue ) . The different intensity of each colour ( red , green and blue ) is determined by its value . This means different hexadecimal represent different colours .

 
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