Data as the computer sees it 1. Number systems Number systems Data storage Data storage Glossary Glossary 2.

Data as the computer sees it

1

Number systems Data storage Glossary

2

Because of their electronics, computers work with only two states – on or off, that is a binary or base 2 number system

3

2358 10101012

A2CD3E1

6

4

Decimal number (base 10): 4192.304

Number 4 1 9 2 . 3 0 4

Placeholder column

3 2 1 0 -1 -2 -3

Place value/Written as base

103 102 101 100 10-1 10-2 10-3

Place value

1000 100 10 11/10=0,1

1/100=0,0

1

1/1000

=0,001

Expanded notation

4192.304=4 X 103+1 X 102+9 X 101+2X100+3X10-1+0X10-

2+4X10-3

=4000+100+90+2+0.3+0+0.004=4192.304

5

Binary number (base 2): 1101.101

6

Hexadecimal numbers (base 16)

7

Engineers discovered that it was easy, from a ‘physical’, engineering point of view, to have just two states – on or off.

This could easily be represented by the presence or absence of current flow.

Hence at the lowest level, data is represented in binary, to make it easier to design and build hardware.

8

Convert binary numbers to decimal numbers

10012= (1 x 23) + (0 x 22) + (0 x 21) + (1 x 20)= (1 x 8) + (0 x 4) + (0 x 2) + (1 x 1) = 8 + 1= 9

Calculator.mp4

9

Convert the following binary numbers to decimal numbers, showing all your calculations.

10

Convert hexadecimal to decimal number

2F316 = (2 x 162) + (F x 161) + (3 x 160)= (2 x 256) + (15 x 16) + (3 x 1)= 512 + 240 + 3= 755

11

Convert the following hexadecimal numbers to decimal, showing all your calculations.

12

This is good old primary

school division with the

remainder!

13

Convert the following decimal numbers to binary numbers.

14

634 ÷ 16 = 39 remainder 10 39 ÷ 16 = 2 remainder 72 ÷ 16 = 0 remainder 2

answer is 27A16 (10 = A)

15

Write the following decimal numbers in hexadecimal notation.

16

Each of these data types is allocated a fixed number of what is termed bytes.

Each byte (a number in binary format e.g. 101100112) in turn, consists of 8 binary digits or bits.

Here is an example of data stored in 4 bytes of 8 bits each, i.e. 32 bits.

17

Each data type is allocated a fixed amount of space (bytes) to store its associated data

There is therefore a limit on the data that can be stored –more bytes - larger the range and fewer bytes - smaller the range.

18

19

A text or string variable that could store a maximum of 5 characters and was assigned the value ‘Addendum’ to the variable.

Some of the text can be ‘lost’.

We refer to the situation where an integer number is ‘misrepresented’ due to an insufficient number of bits being available, as overflow.

A d d e n

20

Each program/programming language uses different numbers of bytes to store numbers

Decimal or real numbers are normally stored in two parts, namely a ‘number’ part and an ‘exponent’ part e.g. 3.1415462973812 x 1012

Obviously, a loss of accuracy in the exponent part would be critical !

A loss of accuracy in the number part would lead to a loss of accuracy in the number of decimals

21

Coding schemes

The ASCII system was the original standard which assigned numeric values to letters, digits, punctuation marks, and other characters

22

Pictures and sound clips

Picture is a collection of thousands of dots, each of which can be modelled by representing its position and colour etc.,then we can digitise any picture or video

Music too can be modelled by representing the data as numerical values describing volume, pitch and frequency

23

Know the basics

24

Apply your knowledge

25

Think and research

26

27