The Patriot missile system was an antimissile system designed to intercept incoming ballistic missiles.

During its early deployment, it often failed to intercept the incoming missiles. The reason was traced toa software error, related to number encoding.

The system gets updates 10 times per second, and thusstores in memory the (integer) number of 0.1 s that have elapsed since the system was turned on.

a) Compute the first 32 digits of the number T=0.1 (in base 2)

b) The memory used in the Patriot missile system stores the variables on 24 bits. Truncate theresult above so you keep only 24 binary digits (23 binary digits past the comma), and convert thecorresponding result into base 10. Let us call this variable T'

c) After n cycles, the true time is , while the time computed by the system is '. Compute the value of n after operating the system for 48 hours, and compute the corresponding cumulatedtime error of the systemd) Compute the corresponding position error, assuming that the missile has a speed of 2000 m/s.