I was studying the conversion technique between Hexadecimal and Binary where
For example
$4C2_{16} = 010011000010_{2}$
Can be done by substituting 4 bits for each Hexadecimal digit.
Why is it so easy to achieve this conversion to binary by combining a series of 4 bits to represent each Hexadecimal digit?
This obviously does not work for decimal to binary conversions, but I am not too sure why either.
For example
$15_{10} ≠00010101_{2}$
Conversion from $2$ to $16$ is simple since $16=2^4$ so every $4$ digits count for one digit.
Meanwhile, bases $10=2\cdot5,16=2^4$ don't have a pattern for exponents of $10$ and $16.$
There is a way to convert bases, though.