# Converting base2 scientific notation to base10 scientific notation

I would now like to know how to convert a value in base2 scientific notation (is that the correct terminology?), say 1.93 * 2 ^ 88, into the form of A * 10 ^ B.

I want to do this without expressing the first form as a complete number and converting it back to the 2nd form.

I can get by exponent by doing 88 * (ln2 / ln10) = 26.49...

So I have A * 10 ^ 26 now.

How can I solve for A?

Complete equation: 1.93 * 2 ^ 88 = A * 10 ^ 26.

This has been moved/duplicated from https://softwareengineering.stackexchange.com/questions/231692/converting-base2-scientific-notation-to-base10-scientific-notation.

You want to convert $a 2^b$ to $c 10^d$. Obviously, you noticed that $d=\lfloor \log (a 2^b)\rfloor$. So, now you need $c$ which is given by $c=a 10^{-d} 2^{b}$ what you get easily using logarithms.
• You are welcome. You got the key part which is $d$. The remaining is just relevant from logarithms. – Claude Leibovici Mar 8 '14 at 16:26