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Number system




Binary number system:

   Computers are the electronic machines which operate using Binary language. Binary system has only two digits to represent or construct entire number system. These digits are 0 and 1 are also called as ON and OFF or TRUE or FALSE. The base of binary number system is 2.

Decimal to Binary:

   To convert Decimal number to Binary simply we divide the Decimal number by 2 and extract the reminder, and co efficient again divided by 2 and extract reminder, repeat this process until the coefficient not able to divide with 2 (That means less than 2 (0 or 1)).

Example:

(225)10    =   (11100001)2  







Binary to Decimal:

   To convert Binary to Decimal number, first we write the binary number and list the powers of 2 from right to left, multiply with position bit and finally add, we get Decimal number.

Example:

1             1           1            0            0             0             0          1
27             26           25           24            23             22              21         20

128  + 64    +  32     +       0       +    0      +      0     +      0      +       1     =  225

Octal number system:

  Octal number system has only eight digits to represent or construct entire number system. These digits are 0, 1, 2, 3, 4, 5, 6 and 7. The Octal number system used in early main frame computers. The base of Octal number system is 8.

Decimal to Octal:

   To convert Decimal number to Octal simply we divide the Decimal number by 8 and extract the reminder, and co efficient again divided by 8 and extract reminder, repeat this process until the coefficient not able to divide with 8 (That means less than 8).

Example:

(225)10    =   (341)8






Octal to Decimal:

   To convert octal to Decimal number, first we write the Octal number and list the powers of 8 from right to left, multiply with position bit and finally add, we get Decimal number.

Example:

 3                4                1
 82                81                80                

192   +    32      +       1   =  225
  
Hexa Decimal number system:

  Hexa Decimal number system has 16 Symbols to represent or construct entire number system. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. The Hexa Decimal number system is 16.

Decimal to Hexa Decimal:

   To convert Decimal number to Hexa Decimal simply we divide the Decimal number by 16 and extract the reminder, and coefficient again divided by 16 and extract reminder, repeat this process until the coefficient not able to divide with 16 (That means less than 16).

Example:

(225)10    =   (E 1)16
 





Hexa Decimal to Decimal:

    To convert Hexa Decimal to Decimal number, first we write the Hexa Decimal number and list the powers of 16 from right to left, multiply with position bit and finally add, we get Decimal number.

Example:

 E (14)       1
  161            160

  224   +   1       =  225



Comments

  1. UnknownAugust 22, 2018 at 5:41 AM

    This comment has been removed by the author.

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  2. UnknownAugust 22, 2018 at 5:45 AM

    Thank you so much sir This is easy to understand

    ReplyDelete
  3. umairMarch 5, 2019 at 11:44 AM

    A number is a concept that arises from the result to have things that are an aggregate or a generalization of this concept.
    numbers information

    ReplyDelete
  4. quyenAugust 2, 2019 at 12:12 AM

    Excellent article. Very interesting to read. I really love to read such a nice article. Thanks! keep rocking.jogos online 2019
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    ReplyDelete

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