In the 1991 Gulf War, the Patriot missile defense system faileddue to round off error. The troubles stemmed from a computer thatperformed the tracking calculations with an internal clock whoseinteger values in tenths of a second were converted to seconds bymultiplying by a 24-bit binary approximation to one tenth:
0.110 ≈ 0.000110011001100110011002
(a) Convert the binary number to a decimal. Call it x.
(You may use Maple convert command: >x:=convert(0.00011001100110011001100,decimal,binary)
(b) What is the absolute error in this number; i.e., what is theabsolute value of the difference between x and 0.1?
(c) What is the time error in seconds after 100 hours ofoperation (i.e., |3,600,000(0.1-x)|)?
(d) During the 1991 war, a Scud missile traveled atapproximately MACH 5 (3750 miles per hour). Find the distance thata Scud missile would travel during the time error computed in(c).
