Page 12 - TP_Prime_V2.2_Class7
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Step 5:  List the last quotient and all the remainders (moving from bottom to top). You will
                            get your binary number.

                  Look at the given examples to understand the conversion better.
                  Example 1: Convert the (26)  to binary number.
                                                  10
                                    2  2 6           The binary equivalent of (26)  is 11010

                                    2  1 3     0
           Prime (Ver. 2.2)-VII     2    6     1     In other words, (26)  = (11010)      2
                                                                                     10
                                                                            10
                                    2    3     0


                                         1      1

                                                     Start  listing  the  last  quotient  and  all  the
                                                     remainders from here.
                  Example 2: Convert the (64)  to binary number.
                                                  10
          10                    2  6 4
                                2  3 2   0

                                2  1 6   0                                       The decimal number system is based
                                2    8   0    (64)  = (1000000)    2               on ten digits, likely influenced by
                                                   10
                                2    4   0                                          the number of human fingers.
                                2    2   0
                                      1    0




                    Binary to Decimal Conversion


                  To convert a binary number into a decimal number, follow 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
                                                                                               2
                                                                                                       1
                                                                              4
                                                                                       3
                                     2
                             3
                      = 1 × 2  + 1 × 2  + 1 × 2  + 1 × 2                = 1 × 2  + 0 × 2  + 1 × 2  + 1 × 2  + 1 + 2 0
                                                     0
                                             1
                      = 8 + 4 + 2 + 1                                   = 16 + 0 + 4 + 2 + 1
                      = 15                                              = 23
                      (1111)  = (15) 10                                 (10111)   = (23) 10
                            2
                                                                               2
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