Question

I mean, for example, I have the following number encoded in IEEE-754 single precision:

"0100 0001 1011 1110 1100 1100 1100 1100"  (approximately 23.85 in decimal)

The binary number above is stored in literal string.

The question is, how can I convert this string into IEEE-754 double precision representation(somewhat like the following one, but the value is not the same), WITHOUT losing precision?

"0100 0000 0011 0111 1101 1001 1001 1001 1001 1001 1001 1001 1001 1001 1001 1010"

which is the same number encoded in IEEE-754 double precision.

I have tried using the following algorithm to convert the first string back to decimal number first, but it loses precision.

num in decimal = (sign) * (1 + frac * 2^(-23)) * 2^(exp - 127)

I’m using Qt C++ Framework on Windows platform.

EDIT: I must apologize maybe I didn’t get the question clearly expressed.
What I mean is that I don’t know the true value 23.85, I only got the first string and I want to convert it to double precision representation without precision loss.

Answer 1

Well: keep the sign bit, rewrite the exponent (minus old bias, plus new bias), and pad the mantissa with zeros on the right…

(As @Mark says, you have to treat some special cases separately, namely when the biased exponent is either zero or max.)