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Example 3: Convert (101.101)  to decimal number.
                                          2
                  Position          2           1           0                      –1          –2         –3

                 Face value         1           0           1           •          1           0           1

                  Weights           2 2        2 1         2 0                     2 –1       2 –2        2 –3

                                                  1
                                         2
                                                          0
                                                                           -2
                                                                  -1
                    101.101 = 1 × 2  + 0 × 2  + 1 × 2  + 1 × 2  + 0 × 2  + 1 × 2   -3
                                   = 1 × 4 + 0 + 1 × 1 + ½ + 0 + 1/8
                                   = 4 + 1 + 0.5 + 0.125
                                   = 5.625
                        (101.101) = (5.625) 10
                                 2


                     Double Tap                                                        Century   #Critical thinking
                                                                                         21 st
                                                                                         Skills
                   1.  Convert the binary number 1000.10 into decimal.








                   2.  Convert decimal number 30 into binary.











                 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                  1    1  1  1  1    _____  Carry bits
                       0             0             0 + 0 = 0
                                                                            1    0  1  1  1  1
                       0             1             0 + 1 = 1
                                                                        +        1  0  1  1  1
                       1             0             1 + 0 = 1

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

            For example, let us add the binary numbers (101111)  and (10111) .
                                                                  2
                                                                               2
                                                                                              #Number System  15
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