In one sense, a digital readout eliminates uncertainty. But since we suspect that time continues to pass during that hour, in another sense digitation increases uncertainty. If we had no analogic notion of time independent of our digital definition, we would always know exactly what time it is by our digital clock. There would simply exist no time between the defined graduations. But if we believe that digital time is merely a convention, and that all the while a real time is continually passing, then we must view digital time as inexact in principle.
Uncertainty is relative to the possibility of a finer-grained cognitive domain.
The causal world of physics appears to us as an analog domain. Nature may be unfathomably rich, or its infinite complexity may be merely an appearance based on limited experience. The advantage of digital communication is that a message can be repeated indefinitely without accumulating error. To put this another way, the advantage of digitation is that only what is intended is transmitted. But this is also its disadvantage, because in one situation some information is gladly discarded as noise, while in another the same lost information may represent a regrettable insensitivity.