Page 16 - TP_Plus_v4_Class7
P. 16

Look at the given examples to understand the conversion better.

              Example 1: Convert the decimal number 26, i.e.,  Example 2: Convert the decimal number 64, i.e.,
              (26)  to binary.                                      (64)  to binary.
                                                                       10
                  10
                2  26                                                               2  64

                2   13    → 0                                                       2  32            → 0

                2    6    → 1                                                       2  16            → 0

                2    3     → 0                                                      2    8            → 0
                                                                                    2    4            → 0
                      1    → 1
                                 Start listing the last quotient                    2    2            → 0
                                 and all the remainders from                              1            → 0
                                 here.
                                                                    The binary equivalent of (64)  is 1000000
                                                                                                 10
              The binary equivalent of (26)  is 11010
                                           10
                                                                    In other words, (64)  = (1000000) 2
                                                                                        10
              In other words, (26)  = (11010) 2
                                  10
                         Interdisciplinary Learning

                         #Mathematics

                 Write the distance between your school and your home in km.
                 Convert this distance in:
                 meter                                                  binary number system


                                                                                                             #Activity



                   BINARY TO DECIMAL CONVERSION


              To convert a binary number into a decimal number, follow these steps:
                  Start from the right-most digit known and count the power of 2 from right to left, starting from 0.

                   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.

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

              The given examples will help you understand the conversion.
              Example 1: Convert (1111)  to decimal number.         Example 2: Convert (10111)  to decimal number.
                                                                                                2
                                          2
                                                                                     4
                                                                                                     2
                                                                                             3
                                                                                                             1
                              = 1 × 2  + 1 × 2  + 1 × 2  + 1 × 2              = 1 × 2  + 0 × 2  + 1 × 2  + 1 × 2  + 1 + 2 0
                                                        1
                                                2
                                        3
                                                                0
                              = 8 + 4 + 2 + 1                                 = 16 + 0 + 4 + 2 + 1
                                   = 15                                       = 23
                         (1111)  = (15) 10                            (10111)  = (23) 10
                               2
                                                                            2
                  14  Plus (Ver. 4.0)-VII
   11   12   13   14   15   16   17   18   19   20   21