“I’ve noticed my Cool Edit software reports clipping on some manipulations (matrixing M-S recordings to M-S stereo) that should not have added up to an overflow. I’m assuming any two tracks that aren’t clipping should be able to be mixed together if one turns them both down 3 dB, right? I’ve been told that you need some headroom for the calculations so that the carry bit is preserved instead of being truncated. One recommendation was that you need 18-bit resolution to manipulate 16-bit data. Can you clarify this issue? How much headroom should I leave?”
There are a number of potential areas of confusion here. In (very) general terms it is true that for most manipulations of digital audio you need more bit depth than what you expect to use in the desired result. When you begin to add numbers together (as happens when mixing and summing signals) you are naturally going to arrive at larger numbers, and it will likely require greater bit depths to maintain the integrity of those numbers. However, the vast majority of software on the market takes this into account. While you may have 16 or 24 bit audio, the mixing engine in your software (whatever you use – Cubase, Pro Tools, etc.) is set up to be able to deal with much larger numbers. These large numbers are then dithered down at the end to produce the final result at whatever bit depth you happen to be working in.
Designers of these programs are already assuming you are going to be mixing signals together, and that without some precautions this signal combining could overload the mix bus. That’s why the internal bit depth has to be (and usually is) significantly higher than the bit depth of each audio track. You shouldn’t need to turn your tracks down at all to mix them together. You can wreck this process, however, by turning some gain stage up enough to overload it. This may be a master level of some bus, or the level of the destination track. I’m not all that familiar with Cool Edit, but it sounds like this is what is happening. If not, then this seriously calls in to question the math going on inside that software because you are correct in your assumption that two non-clipping tracks turned down by 3 dB should not cause clipping when mixed together.