[From Analog Devices Data Converter Handbook]

I understand why they chose to place the first transition at the 1/2 LSB point but **does that not cause non-linearity?**, since you basically have reduced the probability that a 000 code could occur?

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# ADC Non-Linearity – First Transition at 1/2 LSB Explained

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## Best Answer

Unlike the LSB code, which can only have certain discrete values, the analog input is a real, physical, continuous voltage input, which can go above full scale and below zero (even if that violates existing table or abs max rating). What’s misleading is that the graph makes it look like the analog input range for code 0 is smaller than the others, when in fact it is the same size. It’s just that the left half of the code 0 input voltage range is below zero volts, so it is not show on this graph. If they extended the horizontal axis to include negative input voltage, it would be a straight line extending through the “missing” half of the nominal code 0 range, and continuing at 0 as the lower saturation limit, just like the full scale limit does. When you look at a bipolar ADC transfer function, it’s more obvious because the 0 voltage 0 LSB code point is in the center, with positive and negative full scale staircases in opposite directions. This unipolar ADC transfer function graph just looks weird because of where they stopped the horizontal axis.