CONVERSIONS IN NUMBER SYSTEM

  There are six types of conversions in number system. They are:-

  1. Binary to Octal

  2. Octal to Binary

  3. Binary to Hexadecimal

  4. Hexadecimal to Binary

  5. Octal to Hexadecimal

  6. Hexadecimal to Octal.

→ Binary  to Octal  Conversion 

  a. The base for octal number system is 8 and the base for binary number system is 2  i.e.,          2³=8.

  b. From the above statement we can say that the octal number system can be obtained by       taking the power 3 to the binary number system.

  c. In this conversion three bits are taken at a time and one converted into equivalent octal         number system.

  d. For example:- 

                    Convert the binary number into octal number system.

                                   (110 101 011)₂ 

                    Solution:

                                   (6 5 3)_8.

→ Octal to Binary Conversion

  a. This conversion is the reverse process of the above conversion.

  b. Here we have to convert the given octal number to its equivalent binary number by               writing three bits per each digit.

  c. For Example :-

                     Convert the octal number into binary number system.

                                   (1 2 5)₈

                    Solution:

                                   (001 010 101)_2.

→ Binary to Hexadecimal Conversion 

  a. The base for hexadecimal number is 16 and the base for binary number is 2 i.e.,

       2⁴ = 16.

  b. In this conversion the four bits are converted into corresponding equivalent decimal               number.

  c. For example :-

                            Convert the following binary number to hexadecimal number.

                                   (1101 1110 0111 0010)₂

                             Solution:

                                   (  D         E      7       2)_16.

→ Hexadecimal to Binary Conversion 

 a. This process is the reverse process of the previous conversion.

 b. Here we have to write four bits per each digit present in given hexadecimal number.

 c. For example :- 

                        Convert the following hexadecimal number to binary number.

                                       (3          F           D)₁₆

                        Solution:

                                       (0011     1111   1101)₂.

→  Octal to Hexadecimal Conversion  

   

      a. In this conversion there are two steps. They are:

          i. First we have to convert the octal number into its binary form.

         ii. Now convert this binary number into its equivalent hexadecimal number.

     b. For Example :-

                           Convert the following octal number to hexadecimal number.

                                 (  1       5      7)₈

                          Solution:

                                1^st  step → 001  101  111

                                2^nd step → 0000 / 0110 /1111

                               Answer:  (  0          6         F)₁₆.

→ Hexadecimal to Octal Conversion 

  a. In this conversion there are two steps. They are:

     i. First convert the given hexadecimal number into its binary equivalent.

     ii. Now convert this binary equivalent into its octal equivalent.

  b. For Example :- 

                           Convert the following hexadecimal number to octal number.

                                 (   3        F         D)₁₆

                          Solution:

                                   1^st  step → 0011  1111   1101

                                   2^nd step → 001 / 111 /111 /101

                                   Answer: ( 1       7       7      5)₈.

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