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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
                                       3
                        5
                                4
                                                2
                  = 1 x 2  + 0 x 2  + 1 x 2  + 0 x 2  + 0 x 2  + 1 x 2 0
                                                        1
                  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

                  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 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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