Transform expression from $2^{-n}$ to $x \times 10^{-m}$ I'm trying the understand the concept of how floating number are stored in the computer. While trying to understand it I ran into following kind of transformations:
$2^{-n} \approx x \times 10^{-m}$
For example:
$2^{-1074} \approx 5 \times 10^{-324}$
Can you please explain me how this transformation from the base 2 expression to the base 10 expression is being performed?
Thanks in advance

You want to convert $a\times 2^b$ to $c\times 10^d$. Obviously, you noticed that $d=\lfloor \log (a\times 2^b)\rfloor$. So, now you need $c$ which is given by $c=a\times 10^{-d}\times 2^{b}$ what you get easily using logarithms. Hope it helps. ( Note: The floor function used to find the exponent "d" gives us the integer part of a number.)
