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Example 4: Convert the decimal number          Example  5:  Convert  the  decimal number  (125)
                                                                                                                   10
                 (50)  to binary.                               to binary.
                     10
                                                                                  2  125
                                     2  50                                        2  62  – 1
                                     2  25  – 0                                   2  31  – 0

                                     2  12  – 1                                   2   15  – 1
                                     2    6  – 0                                  2    7  – 1

                                     2    3  – 0                                  1    3  – 1
                                           1  – 1
                                                                                        1  – 1
                 Binary equivalent: 110010                      Binary equivalent: 1111101


                 Example 6: Convert the decimal number          Example  7:  Convert  the  decimal number  (192)
                                                                                                                   10
                 (83)  to binary.                               to binary.
                     10
                                     2  83                                        2  192
                                     2  41  – 1                                   2    96  – 0

                                     2  20  – 1                                   2    48  – 0
                                     2  10  – 0                                   2    24  – 0

                                     2    5  – 0                                  2    12  – 0
                                     2    2  – 1                                  2      6  – 0
                                           1  – 0                                 2      3  – 0

                                                                                          1  – 1

                 Binary equivalent: 1010011                     Binary equivalent: 11000000

                 Binary to Decimal Conversion

                 To convert a binary number into a decimal number, follow the these steps:

                 Step 1       Start from the right-most digit known as the LSD before the fractional point, and
                            move leftwards.
                 Step 2       While doing so, multiply each digit by 2 raised to a particular power. The powers of 2
                            start from 0 and increase to 1, 2, and so on as you move leftwards.

                 Step 3     Add up all the resulting products. You will get your decimal number.

                 The following examples will help you to understand the conversion.
                 Example 1: Convert (1111)  to decimal.            Example 2: Convert (10111)  to decimal.
                                             2                                                   2
                                                                           4
                                                                                                       1
                                                                                              2
                                                                                    3
                                                         0
                             3
                                      2
                                                1
                     = 1 × 2  + 1 × 2  + 1 × 2  + 1 × 2            = 1 × 2  + 0 × 2  + 1 × 2  + 1 × 2  + 1 × 2  0
                     = 8 + 4 + 2 + 1                               = 16 + 0 + 4 + 2 + 1
                     = 15                                          = 23
                     (1111)  = (15)                                (10111)  = (23)
                            2      10                                      2       10

                                                                                               Number System         11
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