mmmmmm
32 bit float isn't the same as 24 bits. The Floating point concept is similar to the way mathematicians and scientists denote very large numbers as a mantissa with an exponent. For example, instead of writing 1,234,567,890,000,000,000 you could write 1.23456789 x10^18 The decimal number part is the mantissa, and the '10 to the power 18' part is the exponent.
In Floating point digital audio, 32 bits are used, with 24 as the mantissa and the other eight to provide the exponent. Hence the resolution of the wanted audio is always maintained at 24 bits (probably where you got the idea that the two formats were the same...), but with a scaling factor so that extremely large or very tiny numbers can be denoted without losing that 24 bit resolution. The theoretical dynamic range of a 32 bit Floating point system is about 1500dB!
And yes, you do need to reapply dither when you convert from 32bits (float or fixed) to 24 bits -- but this usually happens automatically in most systems.
Best to clear up any misconceptions about floating points.
24 bit converters rarely achieve much more than 21 or 22 bits of true resolution, but even so they allow us to restore much of the headroom that we were forced to give up with 16 bit systems. Remember -- good professional analogue mixers provides a nominal headroom of 24dB or more above the zero level, with a noise floor some 90 to 100dB below that. 16 bits couldn't match it, but 24 bits can easily.
What that means is that we can use 24 bit recorders like we used to use analogue equipment -- with HEADROOM.
The biggest advantage is that you don't need to compress on the way in. You might want to for an effect that you are happy to commit to at the recording stage, but that's a choice. In the days of analogue recorders, you had to compress on the way in because they had such poor (in modern terms) signal-noise performance.
Finally, a quick word on the rounding errors thing. Assuming a properly dithered converter, there are no rounding errors. The conversion is entirely linear. The theoretical rounding errors due to quantisation are transformed into random errors by the dither, resulting in a noise floor (although you can still encode and recover signals at levels well below the average noise floor level).
Just like in analogue systems.
Just thought that this would clarify any debates about 16/24 bits and FPs.
Hope it didn't bore too many of you.
