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Computer Bugs - Roundoff Error and the Patriot Missile

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0.10

  • During the Gulf War in 1991, a U.S. Patriot missile failed to intercept an

  • Iraqi Scud missile, and 28 Americans were killed.

  • A later study determined that the problem was caused by the inaccuracy of the binary representation of 0.10.

  • The Patriot incremented a counter once every 0.10 seconds.

  • It multiplied the counter value by 0.10 to compute the actual time. However, the (24-bit) binary representation of 0.10 actually corresponds to 0.099999904632568359375, which is off by 0.000000095367431640625.

  • This doesn’t seem like much, but after 100 hours the time ends up being off by 0.34 seconds—enough time for a Scud to travel 500 meters!

  • Professor Skeel wrote a short article about this.