Take the 2-minute tour ×  How can I convert the number 123.45678
* 10^-22 to the IEEE 745 single-precision floating point
representation? Can you show me the steps?  share|improve this
question See stackoverflow.com/questions/3448777/… –  paxdiablo
Nov 25 '11 at 14:53 add comment  1 Answer  Basically you want
binary scientific notation. That is, you want your number to be
of the form 2α, and you need to split α into its integral and
its fractional part, α = k + β, with β < 1 and k ∈ ℤ.  To find
α, take logarithms: α = log2123.45678 − 22 log210.  The integral
part of the exponent, k, is stored in the exponent field of the
IEEE float (after adjusting by the bias), and the fractional
part 2β is stored in the mantissa (omitting the leading 1).
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