Page 42 - Computer Science Class 11 Without Functions
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Example 2: (1000110)  to (70) 10
                            2
        Face Value       1      0      0      0     1      1      0

        Place value      2 6    2 5    2 4    2 3   2 2    2 1    2 0
                                                     3
                                      5
                               6
                                             4
                                                                   1
                         = 1 × 2  + 0 × 2  + 0 × 2  + 0 × 2  + 1 × 2  + 1 × 2  + 0 × 2 0
                                                            2
                         = 64 + 0 + 0 + 0 + 4 + 2 + 0
                         = 70
        (1000110)  = (70) 10
                 2
        Decimal to Octal Conversion
        To convert a whole decimal number to octal, we follow the following steps:
        1.  Divide the number by 8.

        2.  Note the remainder.
        3.  Repeat steps 3a and 3b until the quotient becomes 0
          3a. Divide the quotient by 8
          3b. Note the remainder
        4.  Write the remainders in reverse order from the binary number.

        Example 3: Convert (450)  to an equivalent octal number.
                               10
              8  450          Remainder
              8   56             2

              8    7             0
                   0             7

            (450)  = (702) 8
                 10
        Octal to Decimal Conversion:
        The steps to convert an octal number to decimal are as follows:

        1.  Write the octal number.
        2.  Below each digit, write its place value, represented as a power of 8.
        3.  Multiply the face value of each digit with its place value.
        4.  Add all values in step 3 to get the decimal number.
        We have already seen in example 3 that (702)  is the octal representation of  the decimal number (450) . So, suppose
                                                8
                                                                                                   10
        we express the octal number (702)  as a decimal number. In that case,  we must get the original number (450)  as
                                        8
                                                                                                             10
        shown below:
        Example 4: Convert (702)  to (450)
                               8       10.
        Face Value       7      0      2
        Place value      8    2  8  1    8  0
                         = 7 × 8  + 0 × 8  + 2 × 8 0
                               2
                                       1
                         = 448 + 0 + 2
                         = 450
                         (702)  = (450)
                              8       10



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