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    The rules for adding two binary digits are given below:

                                                   X               Y                  X + Y
                                                   0               0                0 + 0 = 0
                                                   0                1                0 + 1 = 1

                                                   1               0                 1 + 0 = 1

                                                   1                1           1 + 1 = 10 (carry 1)

                      For example, let us add the binary numbers (101111)  and (10111) .
                                                                           2           2
                                                                            ____
                                                          1   1   1  1  1         Carry bits

                                                          1   0  1  1  1  1
                                                      +       1   0  1  1  1
                                                      1   0   0  0  1  1  0

                      BINARY SUBTRACTION

                      In binary subtraction, the binary number of lower value is subtracted from the binary number of
                      higher value. The following table explains the subtraction of digit Y from digit X. If Y is greater than
                      X, then 1 is borrowed from the next position. When the binary digit 0 borrows 1 from the next most
                      significant digit, it becomes 10. The rules for binary subtraction:

                                               X                  Y                     X – Y

                                               0                  0                   0 – 0 = 0
                                                                                       0 – 1 = 1
                                               0                  1
                                                                             (borrow 1, so that 10 – 1 = 1)
                                                1                 0                    1 – 0 = 1

                                                1                 1                    1 – 1 = 0

                      For example, let us subtract the binary number (111)  from (1000) .
                                                                                          2
                                                                            2
                                                               1     1
                                                                              _____
                                                          0  (10)  (10)  (10)       Borrow

                                                          1    0    0     0
                                                       –       1     1    1

                                                          0    0    0     1

                                                                                                            Life Skills & Values
                                                                Self Reflection

                         Your classmate is facing trouble in understanding the different number systems. He is having a hard
                                                                Self Reflection
                         time doing calculations and converting numbers into different number systems. Will you help him by
                         teaching all the steps in detail?

                       12   Premium Edition-VII

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