Originally Posted by Treva
There'll be a gazillion results.
I prefer trusting people here.
Pan law is just something they put in to confuse the rubes.
(That's not true. But it is why you should take a little more initiative and responsibility for educating yourself. If you just 'trust people' on a 'net BB, you're likely to get your head filled with a truckload of nonsense.
And speaking of a truckload of nonsense, here are my
additional thoughts on FP and DAWs...
With regard to the OP question, using a fixed point system affords the maximum mathematical resolution for the designated number of bits used to store the number -- but, as correctly noted, it is a fixed range.
If you use a floating point system to store such a value, you devote some of that memory to store the 'significant' value, and the rest to store exponent information. It's the exponent information that allows us to 'scale' over a wide range of potential values -- but the precision of the number, whether it's .12345 or 123.45 remains the same.
Again, it's very important to understand that the precision
unlimited. Think of the precision as a range
that can be scaled to much higher or lower values.
So, if you devote 24 bits of memory to store an value, you have a maximum theoretical resolution of 144 dB set to a fixed range. A 32 bit FP system would deliver about the same 144 dB of mathematical resolution but it could be floated so that the maximum value was -20 dB, -200 dB or 20 or 200 DB. But the minimum possible value would still be ~144 dB below the maximum (assuming 24 bits of effective precision).
FWIW, the way FP is used in audio DAWs, a 32 bit FP number can store approximately 25 bits of significant data, with the rest used for exponential scaling. (24 bits for the number, AIRI, and a bit devoted to signifying + or -, since we want to allow values above 0 dB for our DAW purposes.) Common 64 bit FP systems will typically deliver 53 bits, IIRC. (IOW, don't be fooled by the 'coincidence' of a 32 bit FP number providing 24 bits. It's not 'proportional' in a linear sense.) http://en.wikipedia.org/wiki/Floating_point