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I have one computer that copies RAM to EEPROM at power down. At power up it copies EEPROM back to RAM.
Some computers hold "calibration" data in EEPROM. That gets set at the factory and may change once a year.
EEPROM may hold a serial number, set at the factory and is never changed.
Some machines I designed have a "power up counter" and a "hour counter" in EEPROM. We want to know how long this unite has run. Some times we get a broken machine that has run 24X7X365 for 4 years. Some times we get a return that is 4 years old and has only been turned on one and has run for less than a hour. (the last one we service under the 1 year warranty)