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Unformatted text preview: failed to intercept an incoming Iraqi Scud missile. The Scud struck an American Army barracks and killed 28 soldiers. The U. S. General Accounting Ofﬁce (GAO) conducted a detailed analysis of the failure [49] and determined that the underlying cause was an imprecision in a numeric calculation. In this exercise, you will reproduce part of the GAO’s analysis. The Patriot system contains an internal clock, implemented as a counter that is incremented every 0.1 seconds. To determine the time in seconds, the program would multiply the value of this counter by a ½ 24bit quantity that was a fractional binary approximation to ½¼ . In particular, the binary representation ½ is the nonterminating sequence: of ½¼
¼ ¼¼¼½½¼¼½½ ¼¼½½ ¡ ¡ ¡¾ where the portion in brackets is repeated indeﬁnitely. The computer approximated ¼ ½ using just the leading bit plus the ﬁrst 23 bits of this sequence to the right of the binary point. Let us call this number Ü. A. What is the binary representation of Ü ¼ ½? B. What is the approximate decimal value of Ü ¼ ½? 2.4. FLOATING POINT
C. The clock starts at 0 when the system is ﬁrst powered up and keeps counting up from there. In this case, th...
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 Spring '10
 Schultz
 The American

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