Question

A missile uses an internal computer clock to measure time in tenths of a second. The missile guidance system needs the time from launch, in seconds, in order to calculate its distance from the launch site. It obtains this by multiplying the computer clock time by 0.1. So, for example, a reading of 50 tenths of a second is 5 seconds. For one particular missile system, the conversion factor of 0.1 is stored in 8 bits as the binary number 0.000110012.

• i.Convert 0.000110012 to a decimal number, showing each step of your working. Do not round your final answer but write it in scientific notation.

• ii. The missile’s internal computer clock shows 200 tenths of a second. Convert this to seconds using your result from Part (i) of this question. Do not round your answer. The missile guidance system now records that it has travelled for this number of seconds.

• iii. Write down the actual number of seconds the missile has been travelling for.

• iv. The formula ‘distance = speed × time’ gives the distance travelled by an object, given its speed and the time it has been travelling. The speed of this missile is 1700 m/s.

  Use your results from Parts (ii) and (iii) of this question to calculate the difference between the distance the missile guidance system thinks it has travelled and the distance it has actually travelled. Write your answer rounded to the nearest tenth of a metre.

[This illustrates a scenario that occurred in 1991 on a US Patriot missile; although, in this case, the conversion of 0.1 was approximated using 24 bits rather than 8 bits. The resulting imprecision caused the missile to miss its target by over 500 m which then hit an army base, killing 28 US service men].