# How many bits should be employed to obtain a resolution

1. May 31, 2014

### killersanta

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. May 31, 2014

### SteamKing

Staff Emeritus
0.01 / 100 = 0.0001 not 0.001

3. May 31, 2014

### 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?

4. May 31, 2014

### SteamKing

Staff Emeritus
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