what is 324 base 5 to base 8

Question

How do you convert 324 base 5 to base 8

Answer 1

A computer can do this directly; so can computer “geeks.”  The rest of us convert the number from base 5 to base 10 (decimal), then into base 8 (octal).  Let’s do that:

    3 2 4 (base 5) =  3*5² + 2*5¹ + 4*5⁰     (powers of the base 5)

                                  3*25  + 2*5  + 4*1

                                      75 + 10 + 4

                                          89  (decimal)

 

To convert 89 (decimal) into Octal, divide by 8 (the new base) and keep the remainder:

            8 into 89 is  11      remainder 1       (c)

                  8 into 11 is 1     remainder 3      (b)

                   8 into 1 is 0     remainder 1       (a)

      Read these from bottom to top (abc):   1 3 1 (Octal)