With both analog and digital clocks, I look at it and I know the time in a subjective instant, the same as I can look at any word of English and know what word I am looking at. There is no internal process I am conscious of. I guess that's what 55 years of practice does.

BTW, lecture theatres often contain large wall-mounted clocks. In my experience they are almost always analog, even if the display itself is electronic. So are public clocks mounted on buildings. An advantage of analog clocks for public display is that they look like nothing except a clock, whereas a digital clock is just a string of digits that could be anything.