There is a type of chip called a Real Time Clock which is specifically designed to use as little power as possible to keep track of time. It is usually connected to a tiny battery or even just a capacitor so that it can keep track of time even when the device is powered off and the main battery is out of power or disconnected. It can also be programmed to send a signal to the device to power on or at least wake up from deep sleep at certain times.
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