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c.  1’s complement of 010111.10 is 101000.01  +1
                         2’s complement of 101000.10 is 101000.10      1    0     0    1     1    0     .    0    1
                         Adding 100110.01 and 101000.10, we get   +    1    0     1    0     0    0     .    1    0
                         Discarding MSB 1 and ignoring leading 0’s
                             (1110.11)                            1    0    0     1    1     1    0     .    1    1
                                 2

                    15.  Perform binary subtraction (1000.01)  -  (110111.1)  using
                                                                 2
                                                      2
                        a.  1’s complement method
                        b.  2’s complement method                         +1                        +1
                   Ans.  a. 1’s complement of 110111.10 is 001000.01            1   0    0    0  .  0    1
                         Adding 1000.01 and 001000.01, we get    +   0    0     1   0    0    0  .  0    1
                         (-101111.01)                                0    1     0   0    0    0  .  1    0
                                   2
                                                                    1’s complement of 010000.10 is 101111.01


                        b. 1’s complement of 110111.10 is 001000.01        +1                        +1
                          2’s complement of 001000.01 is 001000.10               1   0    0    0   .  0   1
                         Adding 1000.01 and 001000.10, we get    +    0    0     1   0    0    0   .  1   0
                         (-101111.01) 2                               0    1     0   0    0    0   .  1   1
                                                                     1’s complement of 010000.11 is 101111.00
                                                                     2’s complement of 101111.00 is 101111.01

                    16.  Perform the octal addition (1567.2)  + (433.4) 8
                                                    8
                   Ans.      +1   +1  +1
                             1    5    6   7   .  2
                         +        4    3   3   .  4
                             2    2    2   2   .  6
                       (2222.6) 8

                    17.  Perform octal subtraction (3214.6)  - (777.7)  using
                                                            8
                                                   8
                        a.  Borrow method
                        b. 7’s complement method
                        c. 8’s complement method
                   Ans.  a.
                                  +8     +8      +8        +8
                           3    2       2    1       1   0       4    3  .  6
                                  7       7       7    .   7
                            2     2       1       4    .   7

                            (2214.7) 8

                       b. 7’s complement of 0777.7 is 7000.0        +1
                           Adding 3214.6 and 7000.0, we get               3    2     1    4   .  6
                           (2214.7)                             +         7    0     0    0   .  0
                                8
                                                                     1    2    2     1    4   .  6
                                                                                                 1
                                                                          2    2     1    4   .  7








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