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

Log tables are what's used by a computer, as noted in the accepted answer.
However, you can approximate powers of two into powers of ten in your head, if you know that:
$2^{10} = 1024 \approx 1000 = 10^3$
This is a very rough approximation, but worth knowing.  It gets you in the right neighborhood.
Applying it to $2^{-1074}$, we get:
$2^{-1074} = 2^{-4} \times 2^{-1070} = 2^{6} \times 2^{-1080} = 2^{6} \times (2^{10})^{-108} \approx $
$2^{6} \times (10^3)^{-108} = 2^{6} \times 10^{-324} = 64 \times 10^{-324} \approx 6 \times 10^{-323} $
However, the rounding error involved adds up to a full order of magnitude in this case; the approximation given in your question is more accurate:
$5 \times 10^{-324}$
Still, this method is worth knowing for sanity-checking an answer within a few orders of magnitude in your head.
