Page 54 - Computer Science Class 11 Without Functions
P. 54

Example 25: Convert (0.1) to its equivalent octal number.
                               10
                                       Fraction part     Integer part

          0.1 ×  8  =     0.8              0.8                0
          0.8 ×  8  =     6.4              0.4                6

          0.4 ×  8  =     3.2              0.2                3
          0.2 ×  8  =     1.6              0.6                1

          0.6 ×  8  =     4.8              0.8                4
          0.8 ×  8  =     6.4              0.4                6

          0.4 ×  8  =     3.2              0.2                3
          0.2 ×  8  =     1.6              0.6                1
          0.6 ×  8  =     4.8              0.8                4

          (0.1)  = (0.063146314…)  = (0.06314) 8
                                 8
               10
                  ↓
               Recurring digits
        The digits in bold are recurring digits. We truncate the recurring digits as per the requirement of accuracy.




                 Find decimal representation of (0.11) , (0.101)  and (0.111) .
                                              2       2         2


        Decimal Numbers having Integer Part and Fraction Part To Octal number

        To convert decimal numbers that have both an integer (whole number) and fractional part, the steps are as follows:
        1.  Convert the integer part to an equivalent octal number (say, a)
        2.  Convert the fraction part between 0 and 1 to an equivalent octal number between 0 and 1 (say, b).
        3.  Put the octal representation of the integer part and the fraction part adjacent to each other.

        Example 26: Convert (902.7421875)  to its octal equivalent.
                                        10
             8   902        Remainder

             8   112            6
             8    14            0
                                          = (1606)
             8     1            6                 8
             8     0            1

                                       Fraction part     Integer part
          0.7421875 × 8 = 5.9375          0.9375              5
          0.9375 × 8        = 7.5          0.5                7

          0.5 × 8              = 4.0       0.0                4
          (0.7421875)  = (0.574) 8
                      10
          So, (902.7421875) = (1606.574) 8
                           10






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