"I was recently involved in a studio session where it became necessary to transfer material from some 20 bit ADATs over to of the client's 16 bit Tascam DA-88s. We did the transfer through the studio's digital mixer, which happened to have both light pipe and TDIF on it. The transfer went fine and the material sounds good on the DA-88s, but we were wondering what happened to those extra bits?"
In a digital transfer of high bit material to a lower bit depth there are basically only two things that can happen to the extra bits: they are either truncated off and thrown away or dither is applied to more elegantly reduce the material to 16 bit words. Which of those happens depends on the hardware and/or software involved in the transfer. For example, if you digitally transfer from a new 20 bit ADAT to an older 16 bit ADAT the extra bits are thrown away. On the other hand, you could bring the material into a DAW at 24 bits (the last four of which wouldn't really be used), dither it down to 16 bits and transfer it to the old ADAT. In your situation it would depend on exactly how your mixer was handling both the reception of the 20 bit audio (was it really receiving at 20 or 24 bits, or just truncating the input?) and the transmission back out to the 16 bit machine. Since Tascam makes 24 bit machines now (and TDIF has always supported 24 bits) you have no way to know what really happened without digging deeper into the functionality of your mixer. This information may or may not be covered in the manual. If not, time to call Tech Support and see what you can learn.
The dithering method is better, but in some circumstances the difference may not be very audible. As is usual in our industry opinions differ on how important this really is. When truncation occurs it is always the least significant bits (LSB) that are removed. Depending upon your recording levels and the average level of the music (not to mention the style of music) the results of truncation may or may not be very pronounced.
Further, there are different types of dither and they don't all sound the same, though the differences are considered by many to be subtle (again depending upon who you talk to). The dither topic is way too deep to get into here, but it's worth mentioning since many people assume it's all the same. It is not, but almost any variety of dither is better than truncation.