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Example 4: (6C.29)  - (71B.D) 16
                               16
              Answer: 15’s complement of 71B.D0 is 8E4.2F                        +1    +1
              16’s complement is 8E4.30
                                                                                       6     C   .  2    9
              Adding 6C.29 and 8E4.30, we get 950.59
                                                                             +    8    E     4   .  3    0
              15’s complement of 950.59 is 6AF.A6                                 9    5     0   .  5    9

              16’s complement of 6AF.A6 is 6AF.A7
              (-6AF.A7) 16


                             Let’s Revisit


                 ♦  Popular number systems are decimal, binary, octal and hexadecimal.
                    ♦ The base of a decimal number system is 10 and digits are 0 to 9.
                    ♦ The base of a binary number system is 2 and digits are 0 and 1.

                    ♦ The base of an octal number system is 8 and digits are 0 to 7.
                    ♦ The base of a hexadecimal number system is 16 and digits are 0 to 9 and A(10), B(11), C(12), D(13), E(14) and F(15).
                    ♦ Calculations like addition, subtraction, multiplication and division can be performed on these numbers.
                    ♦ 1’s complement of a binary number is obtained by replacing 1 with 0 and 0 with 1.

                    ♦ 2’s complement is calculated by adding 1 to 1’s complement.
                    ♦ 7’s complement of an octal number is obtained by subtracting each digit from 7.
                    ♦ 8’s complement is calculated by adding 1 to 7’s complement.
                    ♦ 15’s complement of an octal number is obtained by subtracting each digit from 15.
                    ♦ 16’s complement is calculated by adding 1 to 15’s complement.






                                                            MIND DRILL




                   Solved Questions



              A.  Tick ( ) the correct option:
                  1.  For a number system of base ‘b’, the possible number of digits are ………………… .
                     a.  0 to b                                     b.  1 to b
                     c.  1 to b-1                                   d.  0 to b-1
                  2.  Which of the following is not an example of a binary number?
                     a.  100110                                     b.  200.200
                     c.  1000.0110                                  d.  111.1
                  3.  To express an octal number into its binary equivalent, each octal digit is expressed into ………………… .
                     a.  16 bits form                               b.  4 bits form
                     c.  3 bits form                                d.  8 bits form
                  4.  Which of the following will occupy more memory space?
                     a.  (234)                                      b.  (789)
                                                                           10
                           8
                     c.  (ABC.D)                                    d.  (10011) 2
                             16
                3636  Touchpad Computer Science-XI
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