Changing number bases directly

[elcotufa]

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

 

[LowlyPion]

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

 

[elcotufa]

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

       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

          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 :(

 

[LowlyPion]

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.