A bit can either be a 0 or a 1. Think of it as a light switch, the light is either on or off. Add another to control the brightness, and another and another etc. 16 bits (216) gives you 65536 steps of quantization. 24 bits is 16777216 levels. Thats probably enough resolution, but then there is also 32 bit float. Audio formats have pretty much stopped here, no need to go higher than that, as most people can’t hear the difference between 16 and 24 bit, or 128 vs 320kbs .mp3!
This is the sort of thing that keeps me up at night. Please correct me if I am wrong in my calculation.
I think you could clarify the difference between “steps of quantization” and “levels” as well as what you mean by “float”. It will help people figure out if you’re talking about the same thing or different things altogether. You’re calculations appear to be correct.
To clarify a little:
When I say resolution, steps or levels of quantization, I am saying the same thing in three ways. In binary a number must be rounded to the closest value. The higher the resolution (how many bits are used to record this value) the more acurate this rounding of numbers will be.
32 bit float is often used as the internal recording and processing format within DAW software. Some examples of this are Steinberg Cubase and Image Line FL Studio, they both use a form of 32 bit float. Protools LE uses a 32 bit mixbus, and HD has a 48 bit mixbus.
As for what exactly ‘float’ is I will have to refer you to wikipedia:
http://en.wikipedia.org/wiki/Floating_Point
I think it is quite easy to tell the difference between 128k and 329k MP3 encoding. The tell tale swiching and swooshing at the high end lets you know that. Then there is the smearing of the stereo image and odd phaseyness of sound.
cheers