Re: @ It's understandable...
I haven't a clue what your first paragraph means
The analogue signal representing the waveform you're listening to can take any value between two limits. So you can take any two arbitrarily close values you've already got, and you can put another one inbetween. This is a continuous range.
If you digitise that signal, you can now only represent certain fixed values - for an n-bit word, you only have 2n possible numbers, so that is how many values you can represent. There will be times when the value you wanted to represent is slightly different from the value you actually can represent; you can have an error of up to half the step size between two possible values[1]. This is known as quantisation noise, because it manifests itself as noise on the signal, and is solely down to that signal now being quantised (i.e. discrete), rather than continuous. But half the step size is a very small amount of noise[2].
The advantage of going digital early on is that you are incredibly unlikely to have those numbers changed by noise in the system[3]. But were you to remain in the analogue domain, noise will be added at every step[4]. The upshot of all this is that, although digitisation will necessarily add some noise, it's insignificant alongside the noise you'll get from an analogue system. That's why digital signals in real-world situations give you better fidelity.
Vic.
[1] I'm assuming a simple linear conversion; it's a little more complex to calculate the distortion in a non-linear conversion, but we don't do that in CD players, so I don't care.
[2] And that is the peak error; we can expect a Gaussian distribution of real error
[3] A digital signal can take one of two possible states, some distance apart. If you add noise to that signal, it's trivial to work out the desired state of the signal right up to the point where the noise entirely engulfs the signal. So with that (largely irrelevant) exception, a digital signal is not subject to degradation by noise.
[4] Even if we were to ignore induced noise - which is likely the most significant in an analogue system - there are other noise sources, such as Johnson noise, which cannot be avoided.