Page 49 - Computer Science Class 11 With Functions
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i.  (101011100)  to hexadecimal
                          2
                         added three 0s

                0  0  0  1 0  1  0  1 1  1  0  0

                   1        5         C
                (101011100)  = (15C) 16
                           2
            j.   (F31)  to binary
                    16
                  F          3         1
                  ↓          ↓         ↓
                 1111      0011       0001
                (F31)  = (111100110001) 2
                    16
            k.  (474)  to hexadecimal
                    8
                Step1: Octal to Binary
                  4        7        4
                  ↓        ↓        ↓
                 100      111      100
                (100111100) 2
                Step2: Binary to hexadecimal
                0  0  0  1 0  0  1  1 1  1  0  0

                   1        3         C
                = (13C) 16
                Therefore (474)  = (13C) 16
                              8
            l.   (C8E)  to octal
                    16
                Step1: Hexadecimal to Binary
                  C        8        E
                  ↓        ↓        ↓
                1100      1000     1110
                (C8E)  = (110010001110) 2
                    16
                Step2: Binary to octal
                1  1  0  0    1    0 0    0    1 1    1    0

                  6         2         1        6

                = (6216) 8
                Therefore (C8E)  = (6216)
                              16       8
            2.5.2 Fractional Numbers
            In the previous section, we have discussed how to change the representation of a positive integer from one number
            system to another. Let us now study the conversion of fractional numbers from one number system to another.
            Decimal to Binary Conversion
            To convert a decimal fraction between 0 and 1 (for example, (.25)  and (0.40625) ) to binary, follow the steps given
                                                                      10
                                                                                     10
            below:
              1.  Multiply the fraction by 2.
              2.  Note the integer part of the product (0 or 1).
              3.  Multiply by two; the fraction left over after removing the integer part from the product.

                                                                            Number Systems and Encoding Schemes  47
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