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Step  2    Add up all the resulting products. This sum gives you the decimal number.

                  Example: Convert (101001)  to decimal number.
                                              2
                                4
                        5
                                       3
                                                        1
                                                2
                  = 1 x 2  + 0 x 2  + 1 x 2  + 0 x 2  + 0 x 2  + 1 x 2 0
                  Sum of the products = 32 + 0 + 8 + 0 + 0 + 1 = 41
                  Therefore, (101001)  = (41) 10
                                      2
                            OPERATIONS ON BINARY NUMBERS


                  We can perform various operations on binary numbers. Let's discuss binary addition and binary
                  subtraction in detail.

                  BINARY ADDITION

                  Binary addition is similar to adding 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, the smaller binary number is subtracted from the larger one. The table
                  below illustrates how to subtract digit Y from digit X. If Y is greater than X, we borrow 1 from the
                  next higher position. When a binary digit of 0 borrows 1, it effectively becomes 2 (written as 10 in

                  binary). 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






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