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Most Computers are Digital

  • Recognize only two discrete states: on or off. On means 1 and off means 0.
  • Computers are electronic devices powered by electricity, which has only two states, on or off

Data in computer is represent in binary form. To understand data representation one has to know four number system.
  1. Decimal number system: In this system we use ten different symbol to represent any number. Therefore it’s base is ten. Following are the symbol use in this system. 0, 1, 2 ,3, 4, 5, 6, 7 ,8, 9. (0-9)
  2. Binary number system: In this system we use only two symbols are used. i.e 0, 1. There it’s base is two.
  3. Octal: In this system eight symbol is used i.e 0, 1, 2, 3, 4, 5, 6, 7. Therefore it’s base is eight. (0-7)
  4. Hexadecimal: In this system sixteen symbol is used i.e 0 1 2 3 4 5 6 7 8 9 A B C D E F. Therefore it’s base is sixteen. (0-F)

Conversion From one number system to another

  1. DECIMAL CONVERSION:
    1. Decimal to binary: Divide the given decimal number by 2 till possible and write the remainder in reverse order.
       
      e.g I. (225)10 = (11100001)2
       
    2. Decimal to octal: Divide the given decimal number by 8 till possible and write the remainder in reverse order.
      e.g (225)10 = (341)8
       
    3. Decimal to hexa: Divide the given decimal number by 16 till possible and write the remainder in reverse order.
      e.g (225)10 = (E1)16
       
  2. BINARY CONVERSION
    1. Binary to Decimal
      (11011101)2 = (221)10
       
    2. Binary to Octal: to find the octal value from the binary number,
       
      First method:- convert binary number into decimal number and then divide the decimal number by 8.
       
      Second method:- make the group of three numbers and then find the individual value of that group
       
      e.g (11100001)2 = ( 341 )8
       
      011 100 001 -------- 1st group 001, second group 100 and 3rd group 011.
      Individual value 001 = 1 , 100 = 4, 011 = 3
       
       
      (0 + 2 + 1 = 3) (4 + 0 + 0 = 4) (0 + 0 + 1 = 1) = (341)8
    3. Binary to Hexadecimal
       
      (11011101)2 = (DD)16
       
       
      (1 + 0 + 4 + 8) (1 + 0 + 4 + 8) = (1313)16 = (DD)16
  3. OCTAL CONVERSION
    1. Octal to Decimal
       
      (76)8 = (62)10
       
       
      To find the decimal number from the octal number, position all the number and then multiply with them
    2. Octal to Binary
       
      To convert Octal number to binary, find the binary of individual number in the pair of three digit.
      (76)8 = (111110)2
       
  4. HEXA DECIMAL CONVERSION
    1. Hexadecimal to Decimal
       
      To find the decimal number from the hexadecimal number, position all the number and then multiply with them.
       
      (2AD)16 = (685)10
       
    2. Hexadecimal to Binary
       
      To convert octal number to binary, find the binary of individual number in the pair of four digit.
       
      (2AD)16 = (001010101101)2
       




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