Abe.
That is complete tosh.
If you've enjoyed any sound system playback in the last 10 years, the likelyhood is your listening to a product that has at some point passed through ADC's or DAC's, and has most likely, at some stage been stored in the digital domain.
What digital doesn't do is add sweet things that our ears like to hear like subtle harmonics. Such things look bad on the Scope, but sound wonderful to our ears.
In addition, most digital systems cope with accuracy by adding extra bits to deal with smaller and smaller values (a trick known as "double precision). To put it in perspective, research shows that most humans, at best have a dynamic hearing range of less than 130dB. (that's from the quietest sound we can hear, to near instant hearing damage). The old Vinyl records you may like have a dynamic range nearer to 70dB. CD's... nearer to 96dB.
I believe (and I may have missed something here) that actually makes a CD more accurate at "playing back" your value of 1.5, than an original vinyl LP, or tape for that matter.
However, just in the same way as analog, there is very badly designed digital, and very good designed digital. I've been privy to both, and believe me, when digital is done properly, it's a glorious sound.
Badly designed digital is more about software than about hardware. In digital, we all fear the mighty clipping, when there's no higher to go. (where as in analog, you saturate for a short time, and the analog circuitry will saturate gently, with some wonderful harmonics).
In *good* digital, you allow some extra bits in your databus for clipping, or you do some clever tricks to keep shifting your valuable data within the 24bit realm.
In badly designed digital, multiple clip's or data truncations occur (when you scale the audio lower and lower in the 24 bit word, and start to introduce data truncation). Well designed Digital will ensure that no data is lost, regardless of the amount of headroom you leave in the system.
Once you've gotten past that, then you need to start worrying about jitter in the clocks affecting high frequencies. You can definitely hear a jittery digital system as a harsher, slightly more distorted high frequency range.
Sorry to change topic flow a little hear... it's just that nothing frustrates me more than people taking stabs at the whole digital vs. analog discussion, and throwing a big old opinion out there, without having some understanding of whats going on under the hood.
A bad design, whether it's analog or digital, will make the sound sh*t.
There's just a few more parameters to worry about with digital. Something our friends in the audio interface, mixing software and musical instrument world still continue to learn on a daily basis.