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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)           1    1  1  1  1          Carry bits
                                                                                   1    0  1  1  1  1
                 For example, let us add the binary numbers (101111)
                                                                          2
                 and (10111) .                                                 +        1  0  1  1  1
                             2
                                                                               1  0     0  0  1  1  0
                 Binary Subtraction

                 In binary subtraction, the 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. The rules for binary subtraction:

                         X           Y                   X – Y
                                                                                         1     1
                         0           0                 0 – 0 = 0                                        _____
                                                                                    0  (10)  (10)  (10)       Borrow
                                                       0 – 1 = 1
                         0           1
                                            (borrow 1, so that 10 – 1 = 1)          1    0    0     0
                         1           0                 1 – 0 = 1                 –       1    1     1
                         1           1                 1 – 1 = 0                    0    0    0     1


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



                    To Sum Up


                         The smallest piece of data that can be recognised and used by the computer is known
                        as a bit or a binary digit.

                         A number system is a way to express quantities used for counting, comparing amounts,
                        performing calculations and representing values.
                          A number system made up of ten symbols, 0 to 9, is known as the decimal number
                        system.
                         A number system made up of only two symbols, 0 and 1, is known as the binary
                        number system.

                          A number system made up of eight symbols, 0 to 7, is known as the octal number
                        system.

                          A number system made up of sixteen symbols, 0 to 9 and A to F, is known as the
                        hexadecimal number system.




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                                                                                               Number System
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