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Percentage of error per gain

Hi, 

Does the ratio of gain error and offset error change when the ADC gain is changed?

For example, if the gain is 1 and the gain error is 4% and the offset error is 2%,

Do you think that even if the gain is reduced to 1/6, the gain error will be 4% and the offset error will be 2%?

thank you.

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