Page 58 - Computer Science Class 11 Without Functions
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Example 36: Convert (110.01) to an equivalent octal number.
                                   2
            1    1    0  . 0    1     0


               6         2
            (110.01)  = (6.2) 8
                    2
        Example 37: Convert (110101111.011101110011) to an equivalent octal number.
                                                     2
            1    1    0 1    0    1 1    1    1 0    1    1 1    0    1 1    1    0 0    1    1

               6        5         7        3        5         6        3
            (110101111.011101110011)  = (657.3563) 8
                                     2


                 Find octal representation of (111000.11) (1100110.001010) (111001.000000011) .
                                                 2,
                                                                                   2
                                                                 2,

        Conversion of Octal Numbers to Binary
        To convert an octal number to binary, for each octal digit, write its 3-bit binary representation.

        Example 38: Convert (0.54) to binary
                                 8
                  0  .     5         4
                           ↓         ↓
                          101       100
            = (0.101100) 2
        Example 39: Convert (6.2)  to a binary number.
                               8
              6  .          2
                  ↓        ↓
                 110      010
            = (110.010) 2
        Example 40: Convert (743.456)  to a binary number.
                                    8
                  7        4         3         .        4        5         6
                  ↓        ↓         ↓                  ↓        ↓        ↓
                 111      100       011                100      101      110

            = (111100011.100101110) 2


                 Find binary representation of (6.2) (4.56) and (6.2) .
                                            8,

                                                  8
                                                          8
        Conversion of Binary Numbers to Hexadecimal
        To convert a fractional binary number to its equivalent hexadecimal number, form groups of four bits, starting from left
        to right after the radix point. If the number of bits is not a multiple of four, append the required number of 0's on the
        right end. Finally, replace each group of four bits with an equivalent hexadecimal digit.
        Example 41: Convert (.11011) to its equivalent hexadecimal number.
                                   2
                  three 0s added

            1 1 0    1 1  0  0  0

               D         8
            (.11011)  = (.D8)
                    2      16
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