Page 14 - Trackpad_V5_Book 7
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BINARY ADDITION

            Binary addition is similar to the addition of decimal numbers. When the value of addition exceeds
            the value 1, say 10 or 11, then 1 is carried over to the left of the current position. 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 = 0 (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
                                                                    _____
                                                0  (10)  (10)  (10)       Borrow
                                                1    0    0     0
                                             –       1     1    1

                                                0    0    0     1


                                                                                                    21 st
                                                     Self Reflection                             Century   #Initiative
                                                                                                   Skills
              Your classmate is facing trouble to understand 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   Pro (Ver. 5.0)-VII
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