IZEE UNIT 2

8/8/2019 IZEE UNIT 2

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DATA REPRESENTATIONUnit 2

By: Dipti Purohit

Izee business school bangalore


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UNIT COVERS......

Data Representation,

Binary Data Representation,Binary Coding Schemes:

EBCDIC,

ASCII &UNICODE


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Data FormsData Forms Human communication

Includes language, images and sounds

ComputersProcess and store all forms of data in binaryformat

Conversion to computer-usable representationusing data formats

Define the different ways human data may berepresented, stored and processed by a computer


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Data conversion and representationData conversion and representation


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Data Storage


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Data formatsData formats Proprietary formats

Unique to a product or companyE.g., Microsoft Word, Word

Perfect Standards (evolve in two ways):

Proprietary formats become defacto standards (e.g., Adobe

PostScript)Invented by an internationalstandard organization (e.g.,Motion Pictures Experts Group,MPEG)


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Common Data RepresentationsCommon Data Representations

Type of Data Standard(s)

Alphanumeric Unicode, ASCII, EDCDIC

Image (bitmapped) GIF (graphical image format)

TIF (tagged image file format)

PNG (portable network graphics)

Image (object) PostScript, JPEG, SWF (MacromediaFlash), SVG

Outline graphics and fonts PostScript, TrueType

Sound WAV, AVI, MP3, MIDI, WMA

Page description PDF (Adobe Portable Document Format),HTML, XML

Video Quicktime, MPEG-2, RealVideo, WMV


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Alphanumeric DataAlphanumeric Data

Characters (r, T), numberdigits (0..9), punctuation (!, ;),special purpose characters ($,

&) Four codes/standards torepresent letters and numbers:

BCD (Binary-Coded Decimal)UnicodeASCII (American Standard Codefor Information Interchange)EBCDIC (Extended Binary CodedDecimal Interchange Code)


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Another example is a light fixture Astandard light switch is similar to digital

x It is either on or off 1 or 0

Adimmer light switch issimilar to analogx Its rotating dial can be

turned to many different

positions to make the lightvarying degrees of brightor dim

Data Representation: How do computers

represent data digitally?


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Unlike the decimal system (base 10), the binary numbersystem (base 2) uses only two digits:0 and 1

The following table listssome decimal numbersand their binaryequivalent:

How can a computer represent

numbers?


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Character data is composed of letters, symbols,and numbers that will not be used in arithmetic

operations Numeric data is used in arithmetic calculations, and is

encoded differently

ASCII(American Standard Code for Information

Interchange) requires only7 bits for each character Extended ASCIIuses 8 bits for each character.

Used in most personal computers See the code on the next slide

How can a computer represent words and

letters using bits?


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How can a computer represent words andletters using bits?


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EBCDIC(Extended Binary-CodedDecimal Interchange Code) is an

alternative 8-bit used by older IBM systemsUnicode uses 16 bits and provides codes

for 65,000 characters a bonus forrepresenting alphabets of multiple

languages Used for foreign language support

How can a computer represent words and

letters using bits?


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Sounds and pictures must betransformed into a format the computer

can understandAcomputer must digitize colors, notes,

and instrument sounds into 1s and 0s

For example, a red dot on your screenmight be represented by 1100, a greendot by 1101

How does a computer convert sounds and

pictures into codes?


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Data is stored on a computer in afile Datafiles might contain the text of a document, the

numbers for a calculation, the contents of a web page, orthe notes of a music clip as binary code

Executablefiles contain the programs or instructionsthat tell the computer how to perform a specific task.Forexample, how to display and print text

Data files have afileh

eaderwhich tells thecomputer how the binary code is used to representthe data. The header tells the computer if the binary code

represents a music file, a graphic, a text document, etc.

How does a computer store all these

codes?


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Abitis one binary digit (b) Eg. 0

Abyte is 8 bits (B) Eg. 0010 0100

Anibble is 4 bits Eg. 0011

Quantifying Bits and bytes: How can I tell

the difference between bits and bytes?


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Prefixes Kilo- means a 1000 Mega- means million Giga- means billion

Kilobit (Kb) is approx. 1,000 bits (1,024) Kilobyte (KB) is approx. 1,000 bytes (1,024) Megabyte (MB) is approx. 1,000,000 bytes

(1,048,576) Gigabyte (GB) is approx. 1,000,000,000 bytes

(1,07 ,741,824)

Quantifying Bits and bytes: How can I tell

the difference between bits and bytes?


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1. A(n) _______ device works with discretenumbers, whereas a(n) _______ device works

with continuous data.

2. The _______ number system represents numericdata as a series of 0s and 1s.

3. Most personal computers use the _______ codeto represent character data.

4. 100 Mb is larger than 100 MB. True or false?5. Aprefix that means a million bytes is _______.

Self Quiz Questions


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1. A(n) digital device works with discretenumbers, whereas a(n) analog device works

with continuous data.

2. The binary number system represents numericdata as a series of 0s and 1s.

3. Most personal computers use the extended

ASCII code to represent character data.4. 100 Mb is larger than 100 MB.False

5. Aprefix that means a million bytes is Mega .

Self Quiz Answers


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BinaryConcepts

-- OFF

-- ON

DATA(in binary Digits)


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Data Representation

000111000111010101

011101000110100101010

010010101010101

0100110010001001001

00111100110100101010

100101011010101010000

Main()

{

printf( Hello);

printf(We are enjoying

a world of alphabetical

coding);

}


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Data Representation

Digital computers use binary code to

represent characters.

Binary code is made up of binary

digits or bits. A string of "0s" and "1s" is used to

represent characters.

Byte is a sequence of 8 bits.

Most computers have words thatconsist of 8 or 16 bits.

In large computers the number of bits

per word could be 16 or 32 bits.


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Data representation (Contd.)

When data is keyed in, each keystroke

is converted to a binary character

code and transmitted to the computer

Each character to the printer, screen,

disk is communicated in binary code.

While displaying or printing, the character

is converted back to human readable form


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During calculation the decimal

number is converted to its binaryequivalent.

After calculation the result is

converted back to its decimal

equivalent.

Data Storage (Contd.)


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Number systems The additive approach - Number

earlier consisted of symbols e.g.

Roman number system - I for 1,

II for 2, III for 3 etc.

Positional numbering - Symbols

represent different values depending

on the position they occupy e.g. theDecimal system


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DecimalNumber System

In the decimal number system thesuccessive position to the left of thedecimal point represent units, tens,hundreds, thousands etc.

(3 * 100) + (6*10) + (5*1) = 365 The position of the number affects

its value. These kind of number systems

therefore are called positionalnumber system.

Base

Position number

(6*10)


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DecimalNumber System (Contd.)

The value of each digit in the

number system is determined by:

a) The digit itself

b) The position of the digit

in the number

c) The base/radix of the system


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BinaryNumber System The binary number system has a base of two and

symbols used are 0 and 1. In this number system, as we move to the left,

the value of the digit will be two times greater

than its predecessor because the base is two.

Thus the value of the places are : 64 32 16 8 4 2 1

0001111001010111

Least Significant bit Most Significant bit

Binary Number


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Octal number systems

Binary Octal000 0001 1

010 2011 3100 4101 5

110 6111 7

Uses a base of 8

Values increase

from right to left1, 8, 64, 512 ...


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OctalNumber System

Binary Octal

000 0001 1010 2011 3100 4

101 5110 6111 7

To convert a number from binary to octal andvice versa, the following table must be kept inmind:


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Hexadecimal

NumberSystems

Hexadecimal Decimal0 0

1 12 23 34 45 56 67 78 89 9

A 10B 11C 12D 13E 14

F 15


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Hex. Number Systems(Contd.)

Uses a base of 16 The 16 symbols required for the

hexadecimal number system obtained

by using the alphabets A, B, C,

D, E and F

Converting hexadecimal to decimal

decimal equivalent of a hexadecimal

number A0119(10 * 65,536)+(0 * 4,096)+(1 * 256)+ ( 1 * 16) + ( 9 * 1)

= 6,55,360 + 0 + 256 + 16 + 9

= 6, 55, 641


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Converting binary numbers to decimalvalue


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Divide the decimal number by the

base of the required number system

Note the remainder in one column

and divide the quotient again with the base

Keep repeating this process until quotient is

reduced to a zero Reading remainders in the reverse

order gives the binary equivalent

Decimal to BinaryConversion


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E.g. Converting the decimal number 52to its binary equivalent.

Remainder

2 |__52

2 |__26 | 02 |__13 | 0

2 |__06 | 1

2 |__03 | 02 |__01 | 1

2 |__00 | 1Thus the binary equivalent of the decimal

number 52 is 110100

Decimal to BinaryConversion


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BinarytoHexadecimal

Each hexadecimal digit is representedby 4 binary digits.

Binary Hexadecimal0000 00001 10010 20011 30100 40101 50110 60111 71000 81001 9

1010 A1011 B1100 C1101 D1110 E1111 F


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Binary to Hexadecimal (Contd.)

Split the quantity into groups of fouroutwards from right to left

Each group of four is directly converted into

its hexadecimal equivalentAdd zeros to the left of the number if

necessary

E.g. Binary 10101011000010Hexadecimal Equivalent

0010 1010 1100 0010

2 A C 2


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Hexadecimal to Binary

Write binary equivalent of eachhexadecimal digit in groups of four

E.g. hexadecimal 191A412C

0001 1001 0001 1010 0100 0001 0010 1100 Thus the required binary number can be

written as :

11001000110100100000100101100

The leading zeroes are omitted


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Converting from Binary to Octal

The binary numbermust be divided intogroups of three fromthe octal point- to the

right in case of thefractional portion andto the left in case of theinteger portion.

Each group can thenbe replaced with their

octal equivalent. We may add zero to

the left of the numberif required.

For example :

Binary 101010101010100

101 010 101 010 100

5 2 5 2 4

52524 is the octal

equivalent of the givenbinary number.


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Converting from Octal to Binary

For example :

6 5

110 101

Similarly the binary equivalent of theoctal number 65 is 110101.

Each octal digit is replaced with the appropriatetriple of binary digits.


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ENCODING SCHEMES

In the previous slides, you learnedhow numbers are stored in computers

as binary code.Here is encoding schemes


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Representing Characters

To allow consistent data transfer amongcomputer systems (such as using the ftp

command), rules on how characters are assignedbinary code combinations needed to be created. These rules or encoding standards have

evolved over a period of time and are still

evolving. We will discuss 5 popular encoding standards

ASCII, ISO 8859, EBCDIC, UNICODEandUTF-8.


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Encoding Scheme #1

ASCII (American Standard Code for InformationInterchange) Aconsistent set of rules in which series of 0s and 1s are used to

represent characters. This allows uniformity between data transferamong computer systems.

Evolved from computers that could only work on 7-bit codes at atime.

Computers then evolved into 8-bit machines, thus a leading 0(zero) was placed at beginning to keep originalASCII code, butallowed for additional characters which are often referred to as theextended ASCII character set.

Programmers when writing programs may need to access theseASCII characters (or control codes) by decimal, octal or hexadecimalnumber, so an ASCII table is available to provide assistance. You canissue command man ascii to find out more information regardingthis encoding scheme.


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Encoding Scheme #2ExtendedASCII:ISO 8859 (International Organization for Standards #8859) An encoding scheme to provide additional characters from the

extra bit added to the already existing 7-bitASCII code.

There are sets 1 (ISO 8859-1) and more recently set 15 (ISO 8859-15) which are used to represent most westernEuropean symbols).

Other sets in between include set 2 (ISO 8859-1) use to representmost eastern European symbols and set 10 (ISO 8859-10) used torepresent Lap/Nordic/Eskimo symbols and so forth

ISO 8859 tables are accessible from the internet by performing anet search on ISO 8859 Tables. There are also links on theUNX122 webpage.

You can issue command man iso_8859_1, etc. tofind out more information regarding these encodingschemes.


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Encoding Scheme #3

EBCDIC (Extended Binary Coded DecimalInterchange Code)

An 8-bit binary code used on IBM mainframecomputers. The rules for 0s and 1s in a binary code to

represent characters, differerent from ASCII,but there are programs (including the FTP

command) that can transfer ASCII files toEBCDIC files to allow transfer of data betweendifferent types of computers.

An EBCDIC Table also exists (see link onUNX122 webpage).


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Encoding Schemes for the Future

As economies move to a more globalenvironment there is a move towards anencoding scheme that will simultaneouslyincorporate all the world language symbols intoone large encoding scheme.

This would avoid fragmented encodingschemes previously discussed and allowprograms to easily translate and transfer dataamong different countries.


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Encoding Scheme #4

UNICODE(Universal Character Set / ISO 10646)

16-bit encoding scheme used to represent over65,000 characters.

This encoding scheme will allow most worldlanguage symbols due to the additional 8 bitsin the code.

Unicode is currently in use for many PCs

runningWindows 98 and up, and isconsidered to be the latest trend in datarepresentation to foster global communication.


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IZEE UNIT 2

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