DATA

REPRESENTATION

CHAPTER 2

2.1 DATA TYPES

Different types of data (Fig. 2.1)

The computer industry uses the to define ” MULTIMEDIAterm “

information that contains numbers, text, images, audio and video.

If there’re different types of data..

Do we’ve different types of

computers for each data type

So..

Ex. Is there a computer to process only

numbers

The Answer is: NO

INSIDEDATA 2 .2

THE COMPUTER

DATA

Text Images

Videos Audio

0101101010100

1010101010101

0101010111010

1011010100100

COMPUTER

Bit The smallest unit of data that can be

stored in a computer. it is either 0 or 1

1 = ON

0 = OFF

BIT PATTERN

uniformdata types are transformed into a All

representation when they are stored in a

computer and transformed back to their

original form when retrieved. This universal

representation is called a bit pattern

A Bit pattern made of 16 bits

1000101010111111

How does a computer

memory know what

type of data a stored

bit pattern represents

The Answer is: It Doesn’t It’s the responsibility of input/output

devices or programs

Data Coding & Decoding

BYTE

0 1 0 1 0 0 1 1

Bit Pattern of length 8 = BYTE

Bytes used to measure

the size of memory or

other storage .

2.3 REPRESENTING

DATA

Represent each symbol with bit pattern

TEXT

TEXT

How many bit patterns

we need to represent

the ENGLISH letters

The Answer is: 52 bit patterns 26- Uppercase Letters

26- Lowercase Letters

TEXT

If we’ve an Imaginary

language that uses ONLY

4 symbols. What is the

bit pattern length we need

to represent this language

The Answer is: bit pattern

of length 2

TEXT

Bit pattern length # of Symbols

1 2

2 4

3 8

4 16

.

.

.

.

.

.

16 65,536

TEXT

Different sets of bit patterns have

been designed to represent text

symbols Each set is called a CODE

ASCII:

The American standard code for information interchange . use 7

bit for each symbol

Extended ASCII

To make the size of each pattern 1 byte ( 8 bits)

EBCDIC :

Extended binary coded decimal interchange code. Only IBM main

frames. Uses 8 bits pattern

Unicode

uses 16 bits. To represent more symbols for other languages not

just English

ISO

International Organization for Standardization

Has designed a code using 32bit pattern

Examples of CODES

Examples of CODES

Representing of the word “BYTE” in ASCII code

Numbers are representing using the binary system

before being stored in the computer memory.

as described in Chapter 3.

NUMBERS

Image representation methods

Vector Bitmap

IMAGES

Image divided

into a matrix of

PIXELS ( picture

elements )

where each

pixel is small

dot

An image is

decomposed

into a

combination of

CURVES and

LINES.

Bitmap

IMAGES

Example of representing a black & white image using bitmap

method

Bitmap

IMAGES

Representation of color pixels using bitmap method (8 bit pattern)

B G R 000000000 000000000 11111111

000000000 11111111 000000000

11111111 000000000 000000000

11111111 11111111 11111111

RED

GREEN

BLUE

WHITE

Vector

IMAGES

An image is decomposed into a combination

of curves and lines. Each line or curve

represented by a mathematical formula.

Ex. Representing a LINE by

the coordinates of

it’s end points

IMAGES

Which one is better..

Bitmap method

OR

Vector method

VIDEOS

Is a representation of images (called FRAMES)

in time.

A Movie is a series of frames shown one after

another to create the illusion of motion

If you want to manipulate

bit patterns.

Is it easy for you to write

& remember a long

stream of 0's &1's

The Answer is: NO That’s why we use Hexadecimal OR Octal notations

2.4 HEXADECIMAL

NOTATION

HEXADEC = 16 IN Greek

So.. There are 16 symbols:

HEXADECIMAL NOTATION

F E D C B A 9 8 7 6 5 4 3 2 1 0

A 4- bit pattern can be represented by a

hexadecimal digit, and vice versa.

Hexadecimal

digit

Bit Pattern

8 1000

9 1001

A 1010

B 1011

C 1100

D 1101

E 1110

F 1111

Hexadecimal digits

HEXADECIMAL NOTATION

Hexadecimal

digit

Bit Pattern

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

HEXADECIMAL NOTATION

1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0

F C E 4

1111110011100100 = xFCE4

“x” to show that the representation is in Hexadecimal

Example1:

Show the hexadecimal equivalent of the bit pattern

110011100010.

HEXADECIMAL NOTATION

Example2:

What is the bit pattern for x24C?

HEXADECIMAL NOTATION

2.5 OCTAL NOTATION

OCT= 8 IN Greek

So.. There are 8 symbols:

OCTAL NOTATION

7 6 5 4 3 2 1 0

A 3- bit pattern can be represented by an

OCTAL digit, and vice versa.

OCTAL digits

OCTAL NOTATION

Hexadecimal

digit

Bit Pattern

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

OCTAL NOTATION

1 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0

1 6 3 4

“o” & “0” to show that the representation is in Octal

7 4 o176344

1111110011100100 = 0176344

1763448

Example1:

Show the octal equivalent of the bit pattern

101110010.

OCTAL NOTATION

Example2:

What is the bit pattern for 248?

OCTAL NOTATION