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An article in the Economist a while ago reminds us that not matter how complicated computers are, all they really know is 0 and 1- the binary system. Using the binary system, it is easy to represent these two numbers as on or off on various media.
Back in 2000, the date field on many systems could only hold two digit years, so the year could be 1900 or 2000. As the article explains, the Gangnam Style video on YouTube broke the counter for similar reasons – the counter field had a limited length. In 2038, the date field for many operating systems will also run out. It’s unlikely to be an issue – the Y2K problem wasn’t either – but it does remind us of what underlies all computing devices.