How many bits should be employed to obtain a resolution

In summary, the problem is asking for the number of bits needed for an A/D converter with a full-scale voltage of 10V to obtain a resolution of 0.01%, assuming this refers to the full-scale voltage. With this assumption, the minimum number of bits needed is 17. However, if the 0.01% applies to all readings, then the number of bits needed may be higher. It's important to carry units through calculations to avoid confusion.
  • #1
killersanta
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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 / (2N - 1)


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!
 
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  • #2
0.01 / 100 = 0.0001 not 0.001
 
  • #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?
 
  • #4
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
 
  • #5


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.
 

1. How do you determine the number of bits needed for resolution?

The number of bits needed for resolution depends on the range of values that need to be measured and the desired level of precision. Generally, the more bits used, the higher the resolution.

2. What is the relationship between bits and resolution?

The number of bits directly affects the resolution, as each additional bit doubles the number of possible values that can be represented. For example, 8 bits can represent 256 values, while 16 bits can represent 65,536 values.

3. Can too many bits be employed for resolution?

Yes, using too many bits for resolution can result in unnecessary complexity and cost. It is important to consider the application and the required level of precision when determining the number of bits needed.

4. How does the number of bits impact the accuracy of measurements?

The number of bits used does not necessarily determine the accuracy of measurements. Other factors such as noise, calibration, and instrument design also play a role in accuracy. However, using more bits can improve the potential accuracy by allowing for a finer resolution.

5. Are there any standards for determining the number of bits needed for resolution?

There are no specific standards for determining the number of bits needed for resolution, as it varies depending on the specific application. However, there are guidelines and techniques that can be used to determine the appropriate number of bits for a given situation.

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