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Regarding the following paragraph about resolution of a 16-bit ADC:

Unfortunately, other factors enter the equation to diminish the theoretical number of bits that can be used, such as noise. A data acquisition system specified to have a 16-bit resolution may also contain 16 counts of noise. Considering this noise, the 16 counts equal 4 bits (24 = 16); therefore the 16 bits of resolution specified for the measurement system is diminished by four bits, so the A/D converter actually resolves only 12 bits, not 16 bits.

Above what is meant by “16 counts of noise”? And how does it reduce resolution to 12-bit? Can this be explained in more detail and explicit manner?

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    \$\begingroup\$ Noise measured in LSB's \$\endgroup\$
    – sarthak
    Commented Mar 4, 2019 at 19:06
  • \$\begingroup\$ You have a couple of good answers explaining what "16 counts of noise means". However, your quote is incorrect. The noise does not reduce the resolution of the converter; it reduces the precision (and possibly the accuracy) of the converter. You still get 16 bits from the converter, but you may not be able to get repeatable 16 bit readings. \$\endgroup\$ Commented Mar 4, 2019 at 19:34
  • \$\begingroup\$ @ElliotAlderson I agree I guess they want to say it acts as if 12 bit ADC with zero counts noise. The quote was taken from here under resolution mccdaq.com/TechTips/TechTip-1.aspx \$\endgroup\$
    – user1999
    Commented Mar 4, 2019 at 19:37
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    \$\begingroup\$ The industry term is Effective Number of Bits (ENOB). Added as a comment as neither answer make use of the term. \$\endgroup\$
    – sstobbe
    Commented Mar 4, 2019 at 21:47
  • \$\begingroup\$ With a clean input, the reported output binary code will vary +_8 quanta. \$\endgroup\$ Commented Mar 5, 2019 at 2:59

2 Answers 2

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When talking about ADCs, we often refer to the smallest change in the output as a "count".

16 counts of noise means the numerical value of the digital output value could change by 16 (or maybe by 8 in either direction, or maybe by 16 on average but possibly much more).

But it feels awkward to just say "change by 16" without saying 16 of what. So we say 16 counts, or sometimes 16 lsb's.

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It is something of a tradition to state certain properties of an ADC in comparison to the weight of the least significant bit of the output, or in short form some number (possibly decimal) of LSB's.

The quote is saying that 16 of these counts, or the equivalent of 4 bits, can be expected to consistent of noise. Thus in a simplistic view only the most 12 of the 16 bits seem usable with the lower four containing noise.

However, that may be overly pessimistic. Depending on the nature of the noise and the nature of the signal, you may be able to statistically derive useful information from (or even with aid of) the noise. For example, if the noise is random in a way uncorrelated with the signal and you look at a longer term average, you may be able to deduce a more precise value.

In the right circumstances, this can even let you see things smaller than the least significant bit - for example, if the value is half the least significant bit, and uncorrelated noise is 1 LSB, noise might add with the signal to turn the LSB on half the time, while if it is a third, the LSB might be on a third of the time, and so on.

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