Page 12 - TP-Play_V-2.0_Book-8
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= 1 × 4 + 0 + 1 × 1 + ½ + 0 + 1/8
                      = 4 + 1 + 0.5 + 0.125

                       = 5.625

                              (101.101) = (5.625)
                                   2          10

                OPERATIONS ON BINARY NUMBERS


            Let's learn the basic operations on binary numbers.
            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 = 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, 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.

                                        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


             12       Play (Ver. 2.0)-VIII
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