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Taking another rather large leap forward in time, today's computers (whether PC or Apple or what have you) are running on what's known as Unix Time. (The name "Unix" comes from the fact it was a dominant operating system back when computing was just getting started.) It's based on a 32-bit number and has been counting every second since January 1, 1970.
Once the number reaches 2,147,483,764, however, there's a bit of a problem: When a 32-bit number reaches this value, it can no longer count upwards. Because of this, computers using Unix Time will revert to December 13, 1901 once time hits January 19, 2038, i.e. devices will believe it's the 1900s when it's actually the mid-2000s. The solution? Switch to 64-bit systems, which will run out of values in the year 292,277,026,596.
Is your computer a 32-bit? Do you think there will be any major problems in 2038, or do you think all the important devices will have been replaced with 64-bit by then?
-----The Golden Eagle