The imprecision of floating-point arithmetic can have disastrous consequences if not understood. On Feb 25 1991, a Scud missile struck the American army barracks in Dharan killing 28, even though the barracks were defended by a Patriot missile battery. The Patriot missile failed to intercept the Scud because its internal clock, implemented as a counter that incremented every 0.1 second, had round-off. To determine the time in seconds, the value of the counter (the count) is multiplied by a 24 bit quantity that represents the fractional binary approximation to 1/10 (the leading bit plus the first 23 bits to the right of the binary point) (http://ta.twi.tudelft.nl/users/vuik/wi211/disasters.html) (a) What is the binary representation of 0.1? What did the Patriot's computer approximate as 0.1 (call this r)? (b) Let the Patriot's approximation of 0.1 be r. What is the binary representation of | r-0.1 ? (c) What is the approximate decimal value of |r-0.1 1? (d) The clock starts at zero when the system is first powered-up and keeps counting up from there. In this case, the system had been running for 100 hours. What was the difference between time computed by the Patriot software and the actual time? (e) The system predicts where an incoming missile will appear based on its velocity and the time of last radar sighting. Given that a Scud travels at 2000 m/s, how far off was the prediction? The imprecision of floating-point arithmetic can have disastrous consequences if not understood. On Feb 25 1991, a Scud missile struck the American army barracks in Dharan killing 28, even though the barracks were defended by a Patriot missile battery. The Patriot missile failed to intercept the Scud because its internal clock, implemented as a counter that incremented every 0.1 second, had round-off. To determine the time in seconds, the value of the counter (the count) is multiplied by a 24 bit quantity that represents the fractional binary approximation to 1/10 (the leading bit plus the first 23 bits to the right of the binary point) (http://ta.twi.tudelft.nl/users/vuik/wi211/disasters.html) (a) What is the binary representation of 0.1? What did the Patriot's computer approximate as 0.1 (call this r)? (b) Let the Patriot's approximation of 0.1 be r. What is the binary representation of | r-0.1 ? (c) What is the approximate decimal value of |r-0.1 1? (d) The clock starts at zero when the system is first powered-up and keeps counting up from there. In this case, the system had been running for 100 hours. What was the difference between time computed by the Patriot software and the actual time? (e) The system predicts where an incoming missile will appear based on its velocity and the time of last radar sighting. Given that a Scud travels at 2000 m/s, how far off was the prediction