How to convert numbers to any base?

Does anyone know how to convert one number system directly into another? Is there a general formula for this? Specifically, I need to turn (1101100.11101)₂ into base 4.
🤔 I can't just convert everything to decimal first and then move to this "quaternary" thing—I need to go straight from one to the other, but I have no clue how to do it.

If anyone knows, please help me out.

There are these online tools like
http://number.webmasters.sk/numerical.php
http://www.periodni.com/number_systems_converter.html
As far as I know, there isn't really one universal formula for conversion.
Following some basic logic—I guess—you could convert any base X into decimal (base 10) first, then move from there into base Y. I know direct conversions exist, but the explanations for them seem to depend entirely on which specific bases you're switching between.
http://www.tutorialspoint.com/comput...conversion.htm
https://www.mathsisfun.com/base-conversion-method.html
http://mathforum.org/dr.math/faq/faq.bases.html
This method seems to be the most universal approach, maybe.
http://mathbits.com/MathBits/CompSci...frombase10.htm

You can take the direct route if the bases you're converting between are powers of one another—which is exactly what’s happening here. It makes things pretty straightforward; just group the binary digits into pairs and treat each pair as a single digit in base 4.
That gives you a result of:
1230.322
(Feel free to call me out if I messed up, it's been a minute since I've touched this kind of math)