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Week 09- Numbering System
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Week 09- Numbering System

Week 09- Numbering System

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  • A file system is the underlying structure a computer uses to organize data on a hard disk.
  • A file system is the underlying structure a computer uses to organize data on a hard disk. NTFS is the preferred file system.
  • “ A number system is a term used for a set of different symbols or digits, which represent a numerical value.”
  • It is also called natural number system, because it is natural to humans.

Week 09- Numbering System Week 09- Numbering System Presentation Transcript

  • Week-9
    • Window Installation
      • NTFS vs FAT
    • Digital Representation
      • Coding Scheme
    • Numbering System
      • Binary, Octal, Decimal and Hexadecimal
      • Conversion from one number system to other
        • Binary to Others
        • Decimal to Others
        • Octal to Others
        • Hexadecimal to Others
  • Window XP Installation
    • Window Installation
    • http://www.echoproject.net/en/index.html
  • FAT 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.
  • FAT vs NTFS (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.
    • 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
  • Data Representation (Cont’d)
    • How is a letter converted to binary form and back?
    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 1. The user presses the capital letter D (shift+D key) on the keyboard. Step 4. After processing, the binary code for the capital letter D is converted to an image, and displayed on the output device.
    • 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)
  • Data Representation (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
    • 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 System
  • Types 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.
  • Types of Positional Number Systems No No 0, 1, … 9, A, B, … F 16 Hexa-decimal No No 0, 1, … 7 8 Octal Yes No 0, 1 2 Binary No Yes 0, 1, … 9 10 Decimal Used in computers? Used by humans? Symbols Base System
  • Base or Radix Number Systems
    • 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.
    • 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
      • “ BI nary digi T ” is often referred to by the common abbreviation BIT . 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 (Cont’d)
    • 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 (Cont’d)
    • 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 (Cont’d)
  • Binary Number System Base (Radix) 2 Digits 0, 1 e.g. 1110 2 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=2 3 1 1 0 4=2 2 2=2 1 1=2 0
  • Decimal Number System Base (Radix) 10 Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 e.g. 7475 10 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 1 10
  • Octal Number System Base (Radix) 8 Digits 0, 1, 2, 3, 4, 5, 6, 7 e.g. 1623 8 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=8 3 6 64=8 2 2 8=8 1 3 1=8 0
  • Hexadecimal Number System Base (Radix) 16 Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F e.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=16 3 F 256=16 2 4 16=16 1 D 1=16 0
    • The standard conversion table gives us a quick overview of equivalencies of numbers in different Numbering Systems.
    • Octal Binary
    • 4 2 1
    • 2 2 2 1 2 0
    • 0 0 0 0
    • 1 0 0 1
    • 2 0 1 0
    • 3 0 1 1
    • 4 1 0 0
    • 5 1 0 1
    • 6 1 1 0
    • 7 1 1 1
    Standard Conversion Table
  • Quantities/Counting (1 of 3) 7 7 111 7 6 6 110 6 5 5 101 5 4 4 100 4 3 3 11 3 2 2 10 2 1 1 1 1 0 0 0 0 Hexa- decimal Octal Binary Decimal
  • Quantities/Counting (2 of 3) F 17 1111 15 E 16 1110 14 D 15 1101 13 C 14 1100 12 B 13 1011 11 A 12 1010 10 9 11 1001 9 8 10 1000 8 Hexa- decimal Octal Binary Decimal
  • Quantities/Counting (3 of 3) Etc. 17 27 10111 23 16 26 10110 22 15 25 10101 21 14 24 10100 20 13 23 10011 19 12 22 10010 18 11 21 10001 17 10 20 10000 16 Hexa- decimal Octal Binary Decimal
  • Conversion Among Bases
    • The possibilities:
    Hexadecimal Decimal Octal Binary
  • Quick Example 25 10 = 11001 2 = 31 8 = 19 16 Base
  • Decimal to Decimal (just for fun) Hexadecimal Decimal Octal Binary
  • 125 10 => 5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight
  • Binary to Decimal Hexadecimal Decimal Octal Binary
  • Binary to Decimal
    • Technique
      • Multiply each bit by 2 n , 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
  • Example 101011 2 => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = 32 43 10 Bit “0”
  • Octal to Decimal Hexadecimal Decimal Octal Binary
  • Octal to Decimal
    • Technique
      • Multiply each bit by 8 n , 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
  • Example 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10
  • Hexadecimal to Decimal Hexadecimal Decimal Octal Binary
  • Hexadecimal to Decimal
    • Technique
      • Multiply each bit by 16 n , 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
  • Example ABC 16 => C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 = 2560 2748 10
  • Decimal to Binary Hexadecimal Decimal Octal Binary
  • Decimal 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.
  • Example 125 10 = ? 2 125 10 = 1111101 2 2 125 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 2 0 1
  • Octal to Binary Hexadecimal Decimal Octal Binary
  • Octal to Binary
    • Technique
      • Convert each octal digit to a 3-bit equivalent binary representation
  • Example 705 8 = 111000101 2 705 8 = ? 2 7 0 5 111 000 101
  • Hexadecimal to Binary Hexadecimal Decimal Octal Binary
  • Hexadecimal to Binary
    • Technique
      • Convert each hexadecimal digit to a 4-bit equivalent binary representation
  • Example 10AF 16 = ? 2 10AF 16 = 0001000010101111 2 1 0 A F 0001 0000 1010 1111
  • Decimal to Octal Hexadecimal Decimal Octal Binary
  • Decimal to Octal
    • Technique
      • Divide by 8
      • Keep track of the remainder
  • Example 1234 10 = ? 8 8 1234 154 2 1234 10 = 2322 8 8 19 2 8 2 3 8 0 2
  • Decimal to Hexadecimal Hexadecimal Decimal Octal Binary
  • Decimal to Hexadecimal
    • Technique
      • Divide by 16
      • Keep track of the remainder
  • Example 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4
  • Binary to Octal Hexadecimal Decimal Octal Binary
  • Binary to Octal
    • Technique
      • Group bits in threes, starting on right
      • Convert to octal digits
  • Example 1011010111 2 = ? 8 1011010111 2 = 1327 8 1 011 010 111 1 3 2 7
  • Binary to Hexadecimal Hexadecimal Decimal Octal Binary
  • Binary to Hexadecimal
    • Technique
      • Group bits in fours, starting on right
      • Convert to hexadecimal digits
  • Example 1010111011 2 = ? 16
    • 10 1011 1011
    • B B
    1010111011 2 = 2BB 16
  • Octal to Hexadecimal Hexadecimal Decimal Octal Binary
  • Octal to Hexadecimal
    • Technique
      • Use binary as an intermediary
  • Example 1076 8 = ? 16 1076 8 = 23E 16 1 0 7 6 001 000 111 110 2 3 E
  • Hexadecimal to Octal Hexadecimal Decimal Octal Binary
  • Hexadecimal to Octal
    • Technique
      • Use binary as an intermediary
  • Example 1F0C 16 = ? 8 1 7 4 1 4 1F0C 16 = 17414 8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4
  • Exercise – Convert ... Answer Don’t use a calculator! 1AF 703 1110101 33 Hexa- decimal Octal Binary Decimal
  • Common Powers (1 of 2)
    • Base 10
    T tera 10 12 G giga 10 9 M mega 10 6 k kilo 10 3 m milli 10 -3  micro 10 -6 n nano 10 -9 p pico 10 -12 Symbol Preface Power 1000000000000 1000000000 1000000 1000 .001 .000001 .000000001 .000000000001 Value
  • Common Powers (2 of 2)
    • Base 2
    • What is the value of “k”, “M”, and “G”?
    • In computing, particularly w.r.t. memory , the base-2 interpretation generally applies
    G Giga 2 30 M mega 2 20 k kilo 2 10 Symbol Preface Power 1073741824 1048576 1024 Value
  • Example In the lab… 1. Double click on My Computer 2. Right click on C: 3. Click on Properties / 2 30 =