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    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

                     For example, let us subtract the binary number (111)  from (1000) .
                                                                            2            2
                                                              1     1

                                                         0  (10)  (10)  (10)  _____ Borrow
                                                         1    0     0    0

                                                      –       1     1    1
                                                         0    0     0    1

                     Binary Multiplication

                     Binary  numbers are  multiplied in the same manner  as decimal numbers. When two  binary
                     numbers are multiplied, for each digit of the second number, the product of that digit of the first
                     binary number is calculated. Then it is shifted leftwards so that its rightmost digit lines up with
                     the digit in second number that was used. The sum of all these partial products gives the result.

                     The following rules are followed to multiply two binary numbers.
                                                      X               Y              X × Y
                                                      0               0            0 × 0 = 0

                                                      0               1            0 × 1 = 0
                                                      1               0            1 × 0 = 0

                                                      1               1            1 × 1 = 1

                            For example, let us multiply (1010)  by (101) .
                                                                2         2
                                                                         1  0  1  0

                                                                             1  0   1
                                                                         1  0  1  0
                                                                     0  0  0  0  ×

                                                                  1  0  1  0   ×  ×
                                                                  1  1  0  0  1  0

                                                                                                    Number System        11

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