Three inventions moved clocks and watches away from being mechanical/analogue so they could become digital: The quartz crystal, the circuit board and the liquid crystal display.
Quartz is a common mineral that does this weird thing: it generates a tiny bit of electricity if it’s squeezed, and vibrates when you send an electric charge through it. Watchmakers cut quartz into a shape that looks like a tuning fork, so it vibrates like a tuning fork.
Okay, okay, that was just a gag. You knew that, right? Just a teeny tiny electrical charge passes through the quartz crystal to regulate the watch.
“Inside a quartz clock or watch, the battery sends electricity to the quartz crystal through an electronic circuit. The quartz crystal oscillates (vibrates back and forth) at a precise frequency: exactly 32,768 times each second. The circuit counts the number of vibrations and uses them to generate regular electric pulses, one per second. These pulses can either power an LCD display (showing the time numerically) or they can drive a small electric motor (a tiny stepping motor, in fact), turning gear wheels that spin the clock’s second, minute, and hour hands.” https://www.explainthatstuff.com/quartzclockwatch.html
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