Page 54 - Computer Science Class 11 With Functions
P. 54

(0.1)  = (0.063146314…)  = (0.06314) 8
               10
                                 8
                  ↓
               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)
                      10        8
          So, (902.7421875) = (1606.574) 8
                           10
        Example 27: Convert (902.82)  to its octal equivalent, accurate to three places after the radix point.
                                   10
             8   902        Remainder
             8   112            6
             8    14            0
                                          = (1606)
             8     1            6                 8
             8     0            1

                                       Fraction part   Integer part
          0.82 × 8   =  6.56               0.56            6
          0.56 × 8   =  4.48               0.48            4          =(.643) 8
          0.48 × 8   =  3.84               0.84            3

          (902.82)  = (1606.643) 8
                  10


                 Find octal representation of (3.25) , (20.50)  and (32.125) .
                                            10      10          10




          52   Touchpad Computer Science-XI
   49   50   51   52   53   54   55   56   57   58   59