Electronic clocks work by remembering the time and constantly adding to it. With no power they can't tell how much time passed between being turned off and being turned on again.
Inside a quartz clock or watch, the battery sends electricity to the quartz crystal through an electronic circuit. The quartz crystal oscillates (vibrates back and forth) at a precise frequency: exactly 32768 times each second. The circuit counts the number of vibrations and uses them to generate regular electric pulses, one per second.
Exactly like they said. It's the same with laptops or desktops. If you open them you will see a tiny battery to save the date. Which is called RTC battery. I know that Xbox and Playstation has it as well. My psp has a lil battery but I'm sure it's not for date so idk what is the porpouse yet.
I don't really follow new releases and don't know if MS has the same proclivity for exclusives as Sony, but if they buy a large developer/publisher and all their current and future IPs, it gives them the option to make them exclusive to Xbawx.