how to convert a binary exponent to decimal?

Question

I am stuck with converting the smallest denormalized double precision number which is 2^-1074 to one in the form of power of 10. Any help regarding how can I do this will be appreciated.

Thank You

Answer 1

Use 2^10 approx 10^3 to get 2^1070 approx. 10^(3*107)=10^321 . Combine with 2^4=16 ...

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To get the correct result, compute

log10(2^1074)=1074*log10(2)=323.306215343116

and take the integer part.