The real-time clock (RTC) on the motherboard, powered by the CMOS battery, is responsible for keeping track of time when the system is powered off. However, the RTC does not understand the concept of Daylight Saving Time or time zones – these are managed by the operating system. If the system shows incorrect time, it could be due to the incorrect configuration in the operating system relating to these factors, rather than a hardware issue with the RTC or CMOS battery.