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2
                                                                        -2
                                                   1
                                                                -1
                                                         0
                           101.101 = 1 × 2  + 0 × 2  + 1 × 2  + 1 × 2  + 0 × 2  + 1 × 2 -3
                              = 1 × 4 + 0 + 1 × 1 + 1/2 + 0 + 1/8
                              = 4 + 1 + 0.5 + 0.125
                               = 5.625
                                    (101.101) = (5.625) 10
                                      2


                          Let’s CatCh uP

                    Convert the binary number 1000.10 into decimal.



















                         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               1   1   1  1  1          Carry bits

                         0                1                 0 + 1 = 1              1   0  1  1  1  1
                                                                               +       1   0  1  1  1
                          1               0                 1 + 0 = 1
                                                                               1   0   0  0  1  1  0
                          1               1            1 + 1 = 10 (carry 1)


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


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