Page 57 - Computer Science Class 11 With Functions
P. 57

So, (0.A6) 16   = (0.648) 10   ≠ (0.65) 10   because while converting (0.65) to a hexadecimal number, we discarded the
                                                                         10
            hexadecimal digits appearing beyond two places after the radix point.
            Example 34: Convert (2C1.CF5)  to its equivalent decimal number.
                                        16
            Note that we retain four decimal digits in each computation if only three significant digits after the decimal point are
            required. Thus we may write:
                12
                   = 0.7500
                16
                15   = 0.0585 (truncate after four digits)
                256
                 5   = 0.0012(truncate after four digits)
                4096
            So,  12  +   15   +   5   = 0.75 + 0.0585 + 0.0012 = 0.8097 = 0.809 (truncate after three digits)
               16   256   4096



                    Find decimal representation of (0.2) , (0.4) , (0.C) .
                                                       16
                                                             16
                                                 16

            Conversion of Fractional Binary Numbers to Octal
            To convert a fractional binary number to its equivalent octal number, form groups of three bits, starting from left to
            right after the radix point. If the number of bits is not a multiple of three, append the required number of 0s on the
            right end. Finally, replace each group of three bits with an equivalent octal digit.
            Example 35: Convert (0 .1011)  to an equivalent octal number.
                                       2
                        two 0s added


                .1   0   1 1    0     0

                   5        4
                (.1011)  = (.54) 8
                      2
            Now, let us convert a binary number with both integer and fractional parts to an equivalent octal number.

            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,







                                                                            Number Systems and Encoding Schemes  55
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