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Changing number bases directly

  1. Jan 26, 2009 #1
    1. The problem statement, all variables and given/known data

    How do you change a base into another number directly without changing to base 10 or base 2 for example?

    Eg

    changing 1442 base 6 to base 3 = 112022

    Just want to know the steps in the division

    Teacher wants us to do it this way for less error

    Help appreciated
     
  2. jcsd
  3. Jan 26, 2009 #2

    LowlyPion

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    Homework Helper

    I don't think there there is a formula per se.

    If you are not to convert to base 10 at all, then I think you need to recognize what the digits in base 6 represent in base 3.

    Hence in the ones digits you have
    1,2,3,4,5 base 6 convert to 1,2,10,11,12 base 3.
    10,20, ... base 6 is 20,110,200,220,1010 base 3.
    100, 200, ... base 6 is 1100,2200,11000,12100,20200 base 3
    1000, 2000 ... base 6 is 22000,121000, ... etc. base 3

    Then you can assemble in base 3 least significant first as below to get what the number represents. (But remember you must use base 3 addition to get your result.)

    1442 = 2 + 220 + 12100 + 22000 = 222 + 101100 = 112022
     
  4. Jan 26, 2009 #3
    Thanks, I am kinda getting the idea

    The way I saw it done was dividing 1442 /3 for base 6 to base 3 but the numbers do not match probably

    and for 112022 is by dividing by 20 (number 6 in base 3)

    I'm missing the counting technique when dividing or just suck at it


    This is basicly what he has
    Code (Text):

           11
     3  \ 1442
            332    2
            110    2
             22    0
             4     2
             1     1
             0     1
     
    I can see that 22 times 3 is 66 but 110 in base 3, but I am wondering if there is an easy method, for example counting with the two ones in the top of fours

    from base 3 to base 6 it was
    Code (Text):
     
              202
    20  |   112022
              2101       2
              101        11
                1         11
                0         1

     
    Using leftovers down to top for the number


    There is no method other than knowing what each number is in different bases?

    He could pick base 9 to 16 or something and with fractions and it could get crazy :(
     
    Last edited: Jan 26, 2009
  5. Jan 26, 2009 #4

    LowlyPion

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    Homework Helper

    Yes. That works too if you are up to following the rules of base arithmetic.

    I think I'll stay with base 10 though thank you.

    Good luck.
     
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