How do you change a base directly without using base 10 or base 2?

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To convert a number directly from one base to another without using base 10 or base 2, it is essential to understand the representation of digits in both bases. For example, when converting 1442 from base 6 to base 3, one must recognize how each digit in base 6 translates to base 3. The process involves using base 3 addition to combine the values derived from the base 6 digits. While there is no straightforward formula, understanding the relationships between the bases and performing the necessary arithmetic can yield the correct result. Ultimately, mastering this method can help reduce errors in base conversion.
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Homework Statement



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
 
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elcotufa said:

Homework Statement



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

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
 
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 itThis is basicly what he has
Code:
       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:
          202
20  |   112022
          2101       2
          101        11
            1         11
            0         1

Using leftovers down to top for the numberThere 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:
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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