The 1991 Dhahran Patriot failure came from a clock error that grew with uptime because the system truncated 0.1 in a 24-bit register

The Patriot air-defense system's weapons-control computer tracked time by counting tenths of a second in an integer register and converting that count to a real number by multiplying by 0.1. Because 0.1 has no exact representation in binary, and because the machine's registers were only 24 bits long, the conversion introduced a small truncation error at every step. Per the U.S. General Accounting Office's post-mortem, "the conversion of time from an integer to a real number cannot be any more precise than 24 bits." Crucially, the error was not fixed but cumulative: the longer the system ran without a restart, the larger the absolute clock offset became.

The GAO quantified the drift. Its Appendix II data give a time error of 0.3433 seconds after 100 hours of continuous operation, corresponding to a range-gate shift of about 687 meters — the range gate being the window in which the radar expects to re-find a target it is tracking. A Scud closing at roughly 1,600 m/s traverses that error in a fraction of a second, so a sufficiently drifted clock causes the system to look in the wrong place and fail to confirm the target as a real threat.

On 25 February 1991, Alpha Battery at Dhahran had been running continuously for over 100 hours when it failed to track an incoming Al Hussein (Scud variant); the missile struck a U.S. Army barracks and killed 28 soldiers — the deadliest single Iraqi strike of the war.

This is a concrete, fatal instance of the abstract object at the root of claim-linnainmaa-rounding-error-problem: accumulated floating-point rounding error, the subject Linnainmaa formalized in 1970, here compounding not into a numerical inaccuracy but a body count. It belongs to the same class as claim-cloudflare-2017-leap-second-outage-from-negative-time-delta — software failing because engineers encoded a folk assumption about time — though the mechanism differs: a fixed-point truncation growing without bound rather than a one-off leap-second discontinuity. The failure was diagnosed, and diagnosed in time; what turned a known bug into 28 deaths is treated separately in claim-patriot-dhahran-1991-known-bug-patch-arrived-one-day-late.