3 Patriot missile rounding error (20 points) 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 to a software error and internal computer arithmetic, related to number encoding. We wish to have an internal clock that starts with zero on the system start and measures time in two- tenths of seconds (every 0.2 seconds). Let call T = 0.2. If we believe our clock is perfect, after 300 clock ticks the clock must report that 1 minute has passed (300*0.2 seconds 1 minute). A fixed-point fractional representation was used to store 0.2. In this exercise, we will quantify the impact of storing 0.2 numerically on the missile location difference. a) It has been told that the memory used in the Patriot missile system stores the variables on 8 bit 0.2 register as a fixed point representation. The clock stores 0.2 on an 8-bit register as a fixed-point number with decimal point located after first bit. Compute the first 8 digits of the number T=0.2 in base 2 (one digit before decimal and 7 digits after decimal). x2 2x2 0+1 b) Convert the obtained binary representation from part (a) back into base 10. Let us call this variable T". c) After n clock ticks, the true time is nt, while the time computed by the system is nt'. . For an ideal clock, how many clock ticks should be recorded after the system has operated for 48 hours? Call this number n. b. Compute the time reported by the Patriot missile system clock after n ticks. e. Compute the cumulated time error in seconds by the Patriot missile system's clock. d) Compute the corresponding position error in missile location, assuming that the missile has a speed of 2000 m/s. 3 Patriot missile rounding error (20 points) 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 to a software error and internal computer arithmetic, related to number encoding. We wish to have an internal clock that starts with zero on the system start and measures time in two- tenths of seconds (every 0.2 seconds). Let call T = 0.2. If we believe our clock is perfect, after 300 clock ticks the clock must report that 1 minute has passed (300*0.2 seconds 1 minute). A fixed-point fractional representation was used to store 0.2. In this exercise, we will quantify the impact of storing 0.2 numerically on the missile location difference. a) It has been told that the memory used in the Patriot missile system stores the variables on 8 bit 0.2 register as a fixed point representation. The clock stores 0.2 on an 8-bit register as a fixed-point number with decimal point located after first bit. Compute the first 8 digits of the number T=0.2 in base 2 (one digit before decimal and 7 digits after decimal). x2 2x2 0+1 b) Convert the obtained binary representation from part (a) back into base 10. Let us call this variable T". c) After n clock ticks, the true time is nt, while the time computed by the system is nt'. . For an ideal clock, how many clock ticks should be recorded after the system has operated for 48 hours? Call this number n. b. Compute the time reported by the Patriot missile system clock after n ticks. e. Compute the cumulated time error in seconds by the Patriot missile system's clock. d) Compute the corresponding position error in missile location, assuming that the missile has a speed of 2000 m/s