Given values and the gain of a pressure transducer , how to find the bits req'd for analog/digital conversion

Question

a plane flies at altitudes between 14.7psi(sea level) to 3.6psi(40,000ft).It uses barometric pressure to find altitude. if the gain of the pressure transducer is 600mV/psi & the computer must sense changes in evry 5ft
a. find the no. of bits required for the analog to digital conversion.
b the Full scale value for the converter
c. the resolution of the converter in volts

Answer 1

ok... the resolution is 5ft, so the number of points is 40,000/5 = 8000. 8,000 can be expressed in binary as less than 2^13, so 13 bits are required

Brain is failing me here, the full scale value for 7999 (if scale starts at 0) will be 1111100111111, or for 8000 will be 1111101000000.

resolution in volts is (14.7-3.6)x600/8000 = .8235 mv/5ft

Answer 2

You are looking for a range of 40,000 ft and a resolution of 5 ft. At first glance, you need an A/d with 8000 counts. This would take 13 bits. However, the presure to altitude conversion is probably not linear. to keep your resolution at high altitudes you will need more. My wild guess would be 16 bits. with better math, you might find that 15 bits is enough, but 16 bits is easier to find.
11.1 psi * 600 mV/psi = 6.66 volts.
6.66V / 65536 gives about 100 uv of resolution.
Averaging a lot of samples will reduce the noise in your reading.