Simple. I think of it this way.

Because you're playing digital music, logically there is a maximum and minimum sample (32767 and -32768). If a sound goes through those it's absolutely 100% loud - you can't get any louder. This remains true all the way up to the DAC. When you turn the volume all the way up, this peak is the loudest sound you want to hear.

It therefore makes sense to call that loudest sound '0dB' - i.e. the point at which the signal has not been touched at all (theoretically). Everything below that is [u]quieter[/u] - so we number down from there, going into negative decibels. Likewise, overdriving that signal (i.e. using positive dB) implies that that peak has been amplified too far and has gone past the maximum range the DAC can convert.

This is the other reason why you adjust your amps so 0dB is the loudest you ever want. That way, that loudest sound is still clear and has no distortion (at least from amplification before the DAC stage). You get much less distortion from scaling the signal down than you get from smashing the peaks past that point of no return. (You do get some, since the signal always has 65536 levels of quantisation and dividing down may mean that two levels get converted into one. For instance, with volume half way, 16382 and 16383 will both get smashed to 8191. But the noise introduced is at -96dB, as I understand it, so you're very unlikely to hear it.)

Make sense?

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