Just because it is “turned off” doesn’t mean there is absolutely nothing with power in it. Computers, and by extension consoles, often have a small watch battery on their circuit boards which powers a clock circuit even when the device is turned off. This will allow the device to keep the current time even if it is completely unplugged from the wall, just like a wristwatch could.
The console have a tiny chip in it called a Real Time Clock. It uses very little power and just keeps track of time. The power can come from the mains power through a tiny part of the power supply that never turns off. Or the power can come from a small battery. The battery have enough power to keep the RTC powered for years so even if you put your console in storage it will likely have the time of day fairly accurate when you start it up again.
Two methods.
One is a real time clock. There’s a small battery inside that powers a moderately accurate clock while the console is off and disconnected from power. This clock will be off by a few seconds after a few weeks without power. If you keep it disconnected for enough time, the battery will run out and the clock will reset.
When you turn the console on it will attempt to connect to the internet and synchronize it’s clock using Network Time Protocol (NTP). NTP servers are ran mostly by scientific institutions and provide very accurate time.
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