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Some old-fashioned clocks with digital displays really keep track of the time in an analog fashion.
The electric motor turns two wheels continuously: the faster at a rate of 1 revolution per hour, the slower at a rate of 1 revolution per 24 hours. The wheels move continuously, not in steps.
The faster wheel has connected to it a ring of 60 flat plastic "leaves". On the "leaves" are printed numerals so that, when you hold two adjacent "leaves" apart like an open book, the two open "leaves" spell out a numeral, and flipping a "leaf" increases the number shown by 1 unit. The "book" is opened vertically, and its pages form a ring. This ring is put into position and rotated so that one page falls each minute, showing a new number for the minutes. "Leaves" 45 through 59 have a small tooth on them. The purpose of this tooth is explained later.
The slower wheel has hour numbers printed on it. There are two of each hour, like this: 12am, 12am, 1am, 1am, 2am, 2am, ... 11pm, 11pm. One leaf falls each half-hour, at about 25 and 55 minutes after the hour. (Not necessarily EXACTLY at these times; it is too hard to get the timing right.)
It has been mentioned that the hours do not fall in sync with the minutes. The presence of teeth on the minute leaves has also been mentioned. These teeth are used as follows: At 45 minutes after the hour, the tooth pushes a lever which will catch any falling hour leaf. The lever holds the old hour leaf in place until it is time for the new hour to start.
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