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Forgot to update you all on this (I got distracted by the amount of cool gear you are all getting!):
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The last digit eventually spends more time in 1 than it does on 0, but it's the best I was able to do (I would have loved that to be the other way around, but oh well). Turns out making the last digit match required almost atomic precision.
Anyway, I'm really happy with the instrument. I think it looks great on the bench
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You will never get the last digit to sit on 0 during calibration. It's inherent in the design of most digital systems that the least significanrt bit will flip between 0 and 1. For a counter it depends on when the input signal switches compared to the counting gate in the counter (noise on the level trigger also contributes but is more noticable on high precision countes). The only way you will get a consistent zero is if the internal oscillator and the signal you are measuring are phase locked, but then you are not actually checking the accuracy of the internal oscillator.