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How many bits should be employed to obtain a resolution

  1. May 31, 2014 #1
    1. The problem statement, all variables and given/known data
    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%?


    2. Relevant equations
    Resolution = Full Scale voltage / (2N - 1)


    3. The attempt at a solution

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

    .001 = 10 V / (2N - 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!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 31, 2014 #2

    SteamKing

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    0.01 / 100 = 0.0001 not 0.001
     
  4. May 31, 2014 #3
    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?
     
  5. May 31, 2014 #4

    SteamKing

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    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
     
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