0
$\begingroup$

The number I am trying to convert is 212122101212, from base 3 to base 9.

The way I tried doing it is converting the number to base 10 by multiplying each digit with weight of corresponding power of 3. And then convert this to base 9 by repeatedly diving the number by 9 and keeping the remainder.

Since it's a very large number I committed mistakes couple of times while converting it manually. Is there any better, less error prone, way of converting the number?

$\endgroup$
  • 2
    $\begingroup$ Note that $9 = 3^2$. Can you easily convert a number from base $10$ to base $100$? $\endgroup$ – Daniel Fischer Oct 25 '16 at 13:49
  • $\begingroup$ It doesn't really make sense to convert a number to base 10 as an intermediate step. If you know how to convert form base 3 to 10, then you know how to convert directly from base 3 to any other base. There's nothing special about 10. $\endgroup$ – Jack M Oct 25 '16 at 14:59
0
$\begingroup$

Generally, if you are converting from base $n$ to base $n^m$, you can do it by taking the original number $m$ digits at a time starting from the right.

So in your case, take the number 2 digits at a time starting from the right. $21-21-22-10-12-12$ in base 3 converts to $7-7-8-3-5-5$ in base 9($3^2)$ so your answer is $778355$

$\endgroup$
0
$\begingroup$

$212122101212_3=21|21|22|10|12|12=(2 \times 3+1\times1)3^{10}+(2\times3+1\times1)3^8+(2\times3+2\times1)3^6+(1\times3+0\times1)3^4+(1\times3+2\times1)3^2+(1\times3+2\times1)3^0=7\times9^5+7\times9^4+8\times9^3+3\times9^2+5\times9^1+5\times9^0=778355_9$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.