How many bits should be employed to obtain a resolution

[killersanta]

Homework Statement

An A/D converter is to operate with a full-scale voltage of 10V. How many bits should be employed to obtain a resolution of 0.01%?

Homework Equations

Resolution = Full Scale voltage / (2^N - 1)

The Attempt at a Solution

.01% * 10 V = .01/100 * 10 V = .001

.001 = 10 V / (2^N - 1)

N = 13.2879 = 14 bits

I am just learning this stuff, but 14 bits seems high to me. I believe the mistake is in the Resolution. I am just assuming they me the resolution is .01% of the full scale voltage, this seems wrong to me.

Thanks for any help!

 

[SteamKing]

0.01 / 100 = 0.0001 not 0.001

 

[killersanta]

Wow, thank for the quick reply.

I know that, but don't you times it by 10 V? Isn't the units for resolution volts? I assumed when they said "resolution of 0.01%," I assumed this was .01% of the full scale voltage. Is that wrong to assume?
Should resolution just equal .0001? Then N= 16.6 = 17 bits?

 

[SteamKing]

0.01% of anything is a pretty fine tolerance. 0.01% of 10V is 0.001 V, so the minimum number of bits would be 17, as you calculated. However, the problem statement is not clear if the 0.01% applies only at the maximum voltage. What if you want 0.01% of a 1-V reading?

Note: it's always important to carry the units thru your calculations, so that it's clear thet 0.01% of 10 V = 0.001 V

 

[rezeew]

I would advise double checking the given information and making sure that the resolution required is indeed 0.01% of the full-scale voltage. If that is the case, then your calculations are correct and 14 bits would be needed to achieve this level of resolution. However, it is always important to consider the practicality and cost of using a higher number of bits. If a slightly lower resolution is acceptable, it may be more feasible to use a lower number of bits. Additionally, considering factors such as noise and accuracy in the system may also impact the final decision on the number of bits to be employed. Overall, it is important to carefully consider all factors and requirements before determining the appropriate number of bits for an A/D converter.