I have found that there is a much better way to think of sampled signals than how it is generally presented.
The thinking starts with defining that the signal goes between -1 and +1. Not quite up to one but very close. The signal swings between positive and negative values, up and down with the sound making the music. Not quite reaching 1.0 or -1.0 as that would be where the AD starts clipping.
One sample could then be represented as, exampel, the value 0.123 . In another system the same value could be represented as 0.1234334, clearly a much more accurate description of the value.
So if we simply chop off the last few decimals we can go from 0.1234334 to 0.123, losing precision in describing the sample value. This is how truncation works on the sample level.
But, our ears do not listen to samples, our ears hears the resulting sound vawes. And then things change a bit. The ear never hears one sample by itself, it can only hear the sound created by several samples, maybe even hundreds.
Our ears hears the truncation as two different things.
One effect our ears hears is an increase in the background noise level. This can be expressed as a diminishing of the SN-ratio ( read as Signal to Noise ) .
One way of looking at it, is that below the third decimal ( below 0.001 ) there is only noise.
Another effect our ears hears is the addition of some very low level sound artifacts. Mostly these are masked by all the other sound but sometimes they can be heard.
Notice that this truncation does not involve any scaling or other stuff, it is simply removing decimals from the representation of each sample.
What we want to do with sound samples instead of simply truncation ( = cutting off ) the decimals is to do a process called dithering. The idea is to add a small, specially formed, noise signal before cutting of the decimals in the representation. This special noise signal is designed to make the sound better for the ear. There are several different kinds of dithering signals, suffice to say that they all work about the same way but sound slightly different.
The effect of the dithering is to make the sound more pleasing to the ear, in two different ways.
First the noise floor the ear perceives is moved down a bit. And the ear can actually start hearing things a small way down into the noise floor.
The second effect is that some of the artifacts we hear when truncating are not heard anymore.
// Gunnar