Wednesday, May 23, 2012

Floating Point Digital

A little while ago I decided to finally get my brain wrapped fully around the whole 24/96 concept. And with a lot of searching and reading, and a little help from my friend Fred I was able to sum it up fairly briefly in a post. (24 bits, 96 kHz - What Does It All Mean?) Floating point is another term that gets bandied about a lot lately so I set my sights on that and here's what I came up with. I have to retrace my steps a little bit to get there, but not to the extent that I did in the other article so go read it if this doesn't make any sense.

The digital concept is pretty straight forward. If you have a one bit system digitizing an analog signal, everything louder than 50% gets a 1 and everything lower gets a 0. Two bits gets you four divisions, three bits gets you eight and so on until you get to a sixteen bit system which is 65,000 or so gradations. The problem is that human hearing is pretty sensitive. So to get the best out of a sixteen bit system you have to try and max out your levels when recording to get as much resolution as you can.

Enter twenty-four bit recording. Now you can start at peak level and pull back a whopping 48 dB and you've still got as much resolution as a whole sixteen bit recording just for the quiet stuff! That's the headroom that people are talking about. You can stay well away from peak levels and still get clean, smooth audio. You can bump up the levels later with no penalty because the noise floor is just so far down now.

Here's where stuff really starts to get cool. All the processing that we've been looking at so far uses what's called integer math. That's whole numbers. 0, 1, 2, 3, 4 etc. There are no possible steps between zero and one. But with floating point you add a bunch of wonderful new possibilities by adding a decimal. For what reason though? Does it really matter whether that guitar squeelie was a few decimal points louder or softer? Well, no not really. The loud stuff isn't where you hear the difference.

Looking way down at the other end of the spectrum you can now have full twenty-four bit resolution between zero and one! That's an extreme example but if you record subtle things for a living, like bees buzzing or wind chimes in the distance for a movie soundtrack, you have 16.7 million gradations now in any segment of the scale! I don't often use exclamation marks, do you get how big this is? It gets even more ridiculous when you move up to thirty-two bit recording.

The really cool thing is that it gets the "digital-ness" out of the way and the only real boundaries are in the transducers (mics) that you use to pick up your sounds. Our gear is finally able to start to capture the audible world around us with the same finesse as our ears. Human hearing is logarithmic. Without getting to deep into it, that's the reason you can hear a bee buzzing ten feet away and still stand to hear a rock concert. The recording gear is no longer a choking point.

To put it a different way, back in the days of cassette (shudder) you had this awful, hissy medium with terrible dynamic range. Music had to be squashed to fit on it and to make matters worse, manufacturers would actually lower the level so that the consumer would raise the volume and therefore blame some of the hiss on their own actions! I remember having a favorite song on tape that was mixed with a fade out at the end. The singer was kind of ad libbing but you could never quite pick out the words, even with headphones. The same album on CD let you hear all the way down into those quiet sounds. That was just a stepping stone.

And the real glory of it all is that now that recording technology has reached a new and heretofore undreamed of pinnacle... everyone listens to crap from iTunes on cheap buds so whatever man. Have a nice day Brethren of the Knob and Fader! [end of exclamation mark abuse]


  1. A/D converters don't capture floating point, though. The benefits of floating point are largely limited to mixing and processing. Floating point basically can't clip, though you still need to make sure you're keeping your peaks under 0 when you are throwing stuff back out to the real world.

    Floating point is not ideal as a delivery medium either, since it takes more computational power to work with, which increases power drain, and battery-operated devices want to use as little power as possible. This is why compressed audio formats are not considered viable unless they can be implemented using only integer math.

  2. Good point. There's a lot of talk about how much work is wasted when the final product is an MP3 running through bud earphones. But the consensus seems to be that it's still worth doing the best job you can so that high quality playback sounds good on a nice system and the low end stuff should follow along.

  3. Regarding The Mister's point of earbuds; there's always the idea that in the future, larger harddrives and ubiquitous fast internet connections may make data compression irrelevant and higher fidelity earbuds may exist. That's how I see it, anyway.

  4. It's not that good buds don't exist, the absolutely do. It's just that the average listener isn't even bothering to upgrade to $20 buds, much less a fitted pair of multi-driver ones from a reputable manufacturer.


You're the Scotty to our Kirk