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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

$15_{10} ≠00010101_{2}$

mathguy
  • 927

1 Answers1

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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.

Jason Kim
  • 902