but usually analogue! think FP Journe...there is no real technical reason why they couldn't do a jumping seconds digital but the energy needed to turn a disc (as opposed to a second hand) once every second is not insubstantial and there isn't really enough time to "load up" a spring like there is with digital jumping minutes or jumping hours...that's why jump hours are much more common than jump minutes and very few mechanical jumping seconds.
Ironically, the very reason mechanical jumping seconds are difficult, is why quartz (or other electrical or electronic) jumping seconds are necessary - it takes too much mechanical energy over too short a time to load up (a mechanical capacitor) a spring to advance seconds indicators in single jumps; but it takes too much electrical energy to make a second hand "jump" 3, 4, or 5 times every second, as a mechanically driven, constant gear advancing system does in a mechanical watch. The battery just wouldn't last.
But in both cases, all of these "jumping indicators" can be analogue or digital, as noted previously, and analogue or digital can be wandering or (semi-) instant.
Confusing enough?
;-)
TM