Page 12 - Computer Genius Class 07
P. 12

Octal Number System

                  The octal num er system consists o  eight digits  rom   to  .  ence  the  ase o  octal num er system
                  is  .  n this system  the position o  each digit represents a po er o   . Any digit in this system
                  is al ays less than  . Octal num er system is used as a shorthand representation o  long  inary
                  num ers. The num er    1   is not  alid in this num er system as   is not a  alid digit.

                  Hexadecimal Number System

                  The he adecimal num er system consists o  1  digits  rom   to   and A to F. The letters A to F represent
                  decimal  num ers   rom  1   to  1 .  The   ase  o   this  num er  system  is  1 .   ach  digit  position  in
                  he adecimal num er system represents a po er o  1 . For e ample  the num er        is a  alid
                                                                                                           1
                  he adecimal num er.  t is different  rom         hich is se en hundred and si ty  our. This num er
                                                                 1
                  system pro ides shortcut method to represent long  inary num ers.

                  Decimal to Binary Conversion

                  To con ert a decimal num er into a  inary num er   ollo  these steps
                      Divide the decimal number by 2 (the base of the binary number system).

                     Note down the quotient and the remainder.

                     Divide the quotient  obtained again by 2 and note down  the resulting  quotient  and
                     remainder.

                     Repeat the procedure till you reach a quotient less than 2.

                     List the last quotient and all the remainders (moving from bottom to top). You will get

                     your binary number.

                   oo  at the gi en e amples to understand the con ersion  etter.
                  Example 1:  on ert the decimal num er 2   i.e.   2    to  inary.
                                                                        1

                                          2  2

                                          2   1
                                          2            1

                                          2
                                                1       1

                                                            Start listing the last  uotient and
                                                            all the remainders  rom here.

                  The  inary e ui alent o   2    is 11 1
                                               1
                   n other  ords   2       11 1
                                       1           2








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