Week-9Week-9 Window InstallationWindow Installation

NTFS vs FATNTFS vs FAT Digital RepresentationDigital Representation

Coding Scheme Coding Scheme Numbering SystemNumbering System

Binary, Octal, Decimal and HexadecimalBinary, Octal, Decimal and Hexadecimal Conversion from one number system to otherConversion from one number system to other

Binary to OthersBinary to Others Decimal to OthersDecimal to Others Octal to OthersOctal to Others Hexadecimal to OthersHexadecimal to Others

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Window Window XPXP Installation Installation Window Installation

http://www.echoproject.net/en/index.html

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FAT vs NTFSFAT vs NTFS Formatting Formatting a disk means configuring the disk with a file system

so that Windows can store information on the disk. Formatting erases any existing files on a hard disk. If you format

a hard disk that has files on it, the files will be deleted. FAT32 FAT32, were used in earlier versions of Windows operating

systems, including Windows 95, Windows 98, and Windows Millennium Edition.

FAT32 does not have the security that NTFS provides, FAT32 also has size limitations. You cannot create a FAT32 partition greater than 32GB in this

version of Windows, and You cannot store a file larger than 4GB on a FAT32 partition.

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FAT vs NTFS FAT vs NTFS (Cont’d)(Cont’d)

NTFS The capability to recover from some disk-related errors automatically,

which FAT32 cannot. Improved support for larger hard disks. Better security because you can use permissions and encryption to

restrict access to specific files to approved users. Quick format Quick format is a formatting option that creates a new file table on a

hard disk but does not fully overwrite or erase the disk. A quick format is much faster than a normal format, which fully erases any existing data on the hard disk.

A partition is an area of a hard disk that can be formatted and assigned a drive letter.

The terms partition and volume are often used interchangeably. Your system partition is typically labeled with the letter C. Letters A and B are reserved for removable drives or floppy disk drives.

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We already know that inside a computer system, data is stored in a format that can’t easily read by human beings.

This is the reason why input and output (I/O) interfaces are required.

Every computer stores numbers, letters and other special characters in a coded form.

Different sets of bit pattern have been designed to represent text symbols.

Each set is called a code, and the process of representing symbols is called coding.

Digital Representation

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Data Representation Data Representation (Cont’d)(Cont’d)

How is a letter converted to binary form and back?

Step 1.The user presses the capital letter D (shift+D key) on the keyboard.

Step 2.An electronic signal for the capital letter D is sent to the system unit.

Step 3.The signal for the capital letter D is converted to its ASCII binary code (01000100) and is stored in memory for processing.

Step 4.After processing, the binary code for the capital letter D is converted to an image, and displayed on the output device.

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Different coding schemes are used like BCD, EBCDIC, ANSI. E.g.

In EBCDIC letter “a” is represented by 10000001

In ASCII letter “a” is represented by 01100001

The standard ASCII code uses now 8-bit to represent 255 symbols including upper-case letters, lower-case letters, special control codes, numeric digits & certain punctuation symbols.

For example A----Z, a----z, 0---9, (,), +, -, *, /, ?, <, >, shift, ctrl, enter etc…

Digital Representation (Cont’d)

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Data Representation Data Representation (Cont’d)(Cont’d)

ASCII EBCDIC Unicode—coding scheme capable of representing all

world’s languages

ASCII Symbol EBCDIC

00110000 0 11110000

00110001 1 11110001

00110010 2 11110010

00110011 3 11110011

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Basic understanding of the number system.

A numbering system defined as “A set of values used to represent quantity.”

e.g. The number of students attending class, the number

of subjects taken per student and also use numbers to represent grades achieved by students in class.

Numbering SystemNumbering System

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Types Of Numbering SystemTypes Of Numbering System

NON-POSITIONAL NUMBERING SYSTEM In early days, human being counted on fingers, stones,

pebbles or sticks were used to indicate values. This method of counting an additive approach or the non-

positional number system. In this system, symbols such as I, II, III, IV etc.

POSITIONAL NUMBERING SYSTEM In positional number system, there are only few symbols

called digits, and these symbols represent different values depending on the position they occupy in the number.

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Types of Positional Number SystemsTypes of Positional Number Systems

System Base SymbolsUsed by humans?

Used in computers?

Decimal 10 0, 1, … 9 Yes No

Binary 2 0, 1 No Yes

Octal 8 0, 1, … 7 No No

Hexa-decimal

16 0, 1, … 9,A, B, … F

No No

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Base or Radix Number Base or Radix Number SystemsSystems

• Decimal Base = 10• Binary Base = 2• Octal Base = 8• Hexadecimal (Hex) Base = 16

Each number system has a number of different digits which is called the radix or the base of the number system.

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Binary number System The binary number system uses two digits to represent

numbers, the values are 0 & 1. This numbering system is sometime called the Base 2 numbering system. (0,1)2

“BIBInary digiTT” is often referred to by the common abbreviation BITBIT. Thus, a “bit” in a computer terminology means either a 0 or a 1.

This number system is natural to an electronic machines or devices as their mechanism based on the OFF or ON switching of the circuits.

Therefore, 0 represent the OFF & 1 represent ON state of the circuit.

Types of Positional Numbering System Types of Positional Numbering System

(Cont’d)(Cont’d)

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Octal Number System The octal number system uses eight values to represent

numbers. The values are (0, 1, 2, 3, 4, 5, 6, 7)8 the base of this system is eight.

Decimal Number System The word decimal is a derivative of decem, which is the Latin

word for ten. The number system that we use day-to-day life is called the

Decimal number system. OR The most popular & commonly used number system is the

Decimal number system as it supports the entire mathematical & accounting concept in the world.

The base is equal to ten because there are altogether ten digits (1, 2, 3, 4, 5, 6, 7, 8, 9)10

Types of Positional Numbering System Types of Positional Numbering System

(Cont’d)(Cont’d)

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Hexadecimal Number System The hexadecimal number system has 16-digits or symbols

(hexa means six & decimal means 10 so sum is sixteen) are (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F)16 , so it has the base 16.

This system uses numerical values from 0 to 9 & alphabets from A to F.

Alphabets A to F represent decimal numbers from 10 to 15.

Types of Positional Numbering System Types of Positional Numbering System

(Cont’d)(Cont’d)

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Binary Number SystemBinary Number System

Base (Radix) 2Digits 0, 1e.g. 11102

The digit 1 in the third position from the right represents the value 4 and the digit 1 in the fourth position from the right represents the value 8.

1

8=23

1 1 0

4=22 2=21 1=20

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Decimal Number SystemDecimal Number System

Base (Radix) 10Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9e.g. 747510

The magnitude represented by a digit is decided by the position of the digit within the number.

For example the digit 7 in the left-most position of 7475 counts for 7000 and the digit 7 in the second position from the right counts for 70.

7

1000 100

4 7 5

110

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Octal Number SystemOctal Number System

Base (Radix) 8Digits 0, 1, 2, 3, 4, 5, 6, 7e.g. 16238

The digit 2 in the second position from the right represents the value 16 and the digit 1 in the fourth position from the right represents the value 512.

1

512=83

6

64=82

2

8=81

3

1=80

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Hexadecimal Number SystemHexadecimal Number System

Base (Radix) 16Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,

A, B, C, D, E, Fe.g. 2F4D 16

The digit F in the third position from the right represents the value 3840 and the digit D in the first position from the right represents the value 1.

2

4096=163

F

256=162

4

16=161

D

1=160

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The standard conversion table gives us a quick overview of equivalencies of numbers in different Numbering Systems.

Octal Binary4 2 1

22 21 20 0 0 0 01 0 0 12 0 1 03 0 1 14 1 0 05 1 0 16 1 1 07 1 1 1

Standard Conversion TableStandard Conversion Table

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Quantities/Counting (1 of 3)Quantities/Counting (1 of 3)

Decimal Binary OctalHexa-

decimal

0 0 0 0

1 1 1 1

2 10 2 2

3 11 3 3

4 100 4 4

5 101 5 5

6 110 6 6

7 111 7 7

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Quantities/Counting (2 of 3) Quantities/Counting (2 of 3)

Decimal Binary OctalHexa-

decimal

8 1000 10 8

9 1001 11 9

10 1010 12 A

11 1011 13 B

12 1100 14 C

13 1101 15 D

14 1110 16 E

15 1111 17 F

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Quantities/Counting (3 of 3) Quantities/Counting (3 of 3)

Decimal Binary OctalHexa-

decimal

16 10000 20 10

17 10001 21 11

18 10010 22 12

19 10011 23 13

20 10100 24 14

21 10101 25 15

22 10110 26 16

23 10111 27 17Etc.

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Conversion Among BasesConversion Among Bases

The possibilities:

Hexadecimal

Decimal Octal

Binary

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Quick ExampleQuick Example

2510 = 110012 = 318 = 1916

Base

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Decimal to Decimal (just for fun)Decimal to Decimal (just for fun)

Hexadecimal

Decimal Octal

Binary

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12510 => 5 x 100 = 52 x 101 = 201 x 102 = 100

125

Base

Weight

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Binary to DecimalBinary to Decimal

Hexadecimal

Decimal Octal

Binary

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Binary to DecimalBinary to Decimal Technique

Multiply each bit by 2n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the

right Add the results

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ExampleExample

1010112 => 1 x 20 = 11 x 21 = 20 x 22 = 01 x 23 = 80 x 24 = 01 x 25 = 32

4310

Bit “0”

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Octal to DecimalOctal to Decimal

Hexadecimal

Decimal Octal

Binary

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Octal to DecimalOctal to Decimal

Technique Multiply each bit by 8n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the

right Add the results

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ExampleExample

7248 => 4 x 80 = 42 x 81 = 167 x 82 = 448

46810

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Hexadecimal to DecimalHexadecimal to Decimal

Hexadecimal

Decimal Octal

Binary

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Hexadecimal to DecimalHexadecimal to Decimal

Technique Multiply each bit by 16n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the

right Add the results

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ExampleExample

ABC16 => C x 160 = 12 x 1 = 12 B x 161 = 11 x 16 = 176 A x 162 = 10 x 256 = 2560

274810

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Decimal to BinaryDecimal to Binary

Hexadecimal

Decimal Octal

Binary

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Decimal to BinaryDecimal to Binary

Technique Divide by two, keep track of the remainder First remainder is bit 0 (LSB, least-significant bit) Second remainder is bit 1 Etc.

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ExampleExample

12510 = ?22 125 62 12 31 02 15 12 7 12 3 12 1 12 0 1

12510 = 11111012

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Octal to BinaryOctal to Binary

Hexadecimal

Decimal Octal

Binary

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Octal to BinaryOctal to Binary

Technique Convert each octal digit to a 3-bit equivalent binary

representation

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ExampleExample

7 0 5

111 000 101

7058 = 1110001012

7058 = ?2

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Hexadecimal to BinaryHexadecimal to Binary

Hexadecimal

Decimal Octal

Binary

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Hexadecimal to BinaryHexadecimal to Binary Technique

Convert each hexadecimal digit to a 4-bit equivalent binary representation

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ExampleExample10AF16 = ?2

1 0 A F

0001 0000 1010 1111

10AF16 = 00010000101011112

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Decimal to OctalDecimal to Octal

Hexadecimal

Decimal Octal

Binary

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Decimal to OctalDecimal to Octal

Technique Divide by 8 Keep track of the remainder

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ExampleExample123410 = ?8

8 1234 154 28 19 28 2 38 0 2

123410 = 23228

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Decimal to HexadecimalDecimal to Hexadecimal

Hexadecimal

Decimal Octal

Binary

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Decimal to HexadecimalDecimal to Hexadecimal

Technique Divide by 16 Keep track of the remainder

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ExampleExample123410 = ?16

123410 = 4D216

16 1234 77 216 4 13 = D16 0 4

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Binary to OctalBinary to Octal

Hexadecimal

Decimal Octal

Binary

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Binary to OctalBinary to Octal Technique

Group bits in threes, starting on right Convert to octal digits

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ExampleExample10110101112 = ?8

1 011 010 111

1 3 2 7

10110101112 = 13278

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Binary to HexadecimalBinary to Hexadecimal

Hexadecimal

Decimal Octal

Binary

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Binary to HexadecimalBinary to Hexadecimal Technique

Group bits in fours, starting on right Convert to hexadecimal digits

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ExampleExample10101110112 = ?16

10 1011 1011

2 B B

10101110112 = 2BB16

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Octal to HexadecimalOctal to Hexadecimal

Hexadecimal

Decimal Octal

Binary

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Octal to HexadecimalOctal to Hexadecimal Technique

Use binary as an intermediary

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ExampleExample10768 = ?16

1 0 7 6

001 000 111 110

2 3 E

10768 = 23E16

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Hexadecimal to OctalHexadecimal to Octal

Hexadecimal

Decimal Octal

Binary

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Hexadecimal to OctalHexadecimal to Octal

Technique Use binary as an intermediary

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ExampleExample1F0C16 = ?8

1 F 0 C

0001 1111 0000 1100

1 7 4 1 4

1F0C16 = 174148

1 7 4 1 4

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Exercise – Convert ...Exercise – Convert ...

Don’t use a calculator!

Decimal Binary OctalHexa-

decimal

33

1110101

703

1AF

Answer

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Common Powers (1 of 2)Common Powers (1 of 2)

Base 10Power Preface Symbol

10-12 pico p

10-9 nano n

10-6 micro

10-3 milli m

103 kilo k

106 mega M

109 giga G

1012 tera T

Value

.000000000001

.000000001

.000001

.001

1000

1000000

1000000000

1000000000000

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Common Powers (2 of 2)Common Powers (2 of 2)

Base 2Power Preface Symbol

210 kilo k

220 mega M

230 Giga G

Value

1024

1048576

1073741824

• What is the value of “k”, “M”, and “G”?

• In computing, particularly w.r.t. memory, the base-2 interpretation generally applies

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ExampleExample

/ 230 =

In the lab…1. Double click on My Computer2. Right click on C:3. Click on Properties