When converting from a source base (non-decimal) to destination base (non-decimal) why it should be converted to decimal base? Why can’t I directly convert from source to destination base using the same algorithm?
Converting from base x to base y
The formula we have Learned so far only works when either the source base or destination Base is decimal.
Is there a direct algorithm for converting a number from one non-decimal base to another non-decimal base directly?
If you’re going between bases which are exponentially linked, it’s not too bad. For example, going from binary (base-2) to hexadecimal (base-16) isn’t bad, because you can group four binary digits to create a single hex digit, because 2^4 = 16. Even so, you still must convert that group of four bits into decimal first to extract its hexadecimal value, OR memorize the sixteen possible binary values that make up the hexadecimal digit.
However, if you’re going to go between arbitrary bases, I suspect this would be more difficult, and could only be done by converting to decimal first.