This description of the problem appears on the Web site of the Telecommunications Managers Association (Britain). The reason why it is described as catastrophic is because every bad calculatioin must be corrected by hand. This is clearly not possible in human-based systems (such as banks), let alone purely computerized systems. So, the systems that rely on the noncompliant chips or programs will no longer be reliable.
That means all of them.
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The millennium bug or the Year 2000 problem (Y2K) was introduced soon after the commercial introduction of computers. In those days, the 80 positions of punch cards were often a limitation while the required memory was nearly unaffordable. To overcome this, it became common practice to drop the first two digits of the year – 1970 became 70 in the computer. Many systems, hardware and software, still work on this principle nowadays.
As a consequence, the change from 1999 to the year 2000 will cause false results when for example, two dates are subtracted. In real life the result of 2000 minus 1970 will be 30. Inside the computer this will be 00–70=–70. Instead of being 30 years old, you will have to wait 70 years before you are born (again?). For nearly all computer–based (commercial) applications this will lead to catastrophic outcomes.