Most tech that does this has a clock that keeps running when the device is off. On laptops and computers it’s typically powered by a small battery on the motherboard, or sometimes a supercapacitor. Phones will have this circuit, but I think they just run off the battery, they might use a supercap, but I don’t know of any with an extra battery for this.
Not everything actually has that though, a raspberry pi for example doesn’t have one, so when they boot they have no idea what the time is, and typically are configured to just get the time when it gets internet access (when they can find another computer on the internet and ask it for the time). For a lot of internet things, this is how they work (routers, google home, alexa, etc).
Old motherboards had essentially a watch battery inside them that would keep the timekeeping circuit powered; for most clocks, the most power draw is the display and the circuitry for figuring that out (or for an analog clock, the motors rotating the gears to make the hands turn), so a chip whose only job is to keep track of time is pretty low-powered.
Haven’t checked a phone, but it is likely that it keeps some of the battery reserved for that, or runs updates in the background; often even if there’s not enough cell service for a call or text, there’s enough cell service to correct your time. There’s also the time that the GPS will give the phone, though because of relativity those clocks aren’t exactly right. Basically lots of ways for a phone to save/get the time without you knowing.
Generally there will be a special little battery on your main board to do that, at least that’s what a computer does. On your phone, if you unplug your main battery, and then turn it on (without WiFi or Cellular so it can’t get the time from the internet) will it have the correct time? If so, it has a clock battery. If not, it’s just using your regular battery.
There’s a battery in your motherboard. It keeps track of the time you switch off your machine and keeps ticking even when its off keeping a counter.
Once you switch on the machine, it checks the time your pc was turned off, checks the counter, adds it to the previous time and shows you the current time.
This is why when you forget your bios password and reset it by removing the battery, all time and date settings is lost.
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