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What is the purpose of the comparator here? I understand that it must be a normal comparator that when the positive input voltage is greater than the negative input voltage returns a logic 1 at its output. What does this tell the logic conversion block? If the comparator output is 0 (reference voltage greater than the analog pin voltage) what happens? If the comparator output is 1 (analog pin voltage greater than the reference voltage) what happens?

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The shown ADC converter works by stepwise control of the 10-bit DAC, comparing the result with the analog input signal from the mux.

It does this via a "binary chop" / "successive approximation" approach.

First the top bit of the DAC is set, and the comparator used to decide if the input signal is higher or lower. If the input signal is lower, the DAC top bit will be changed to zero. If the input signal is higher, the top bit of the DAC is left as one.

This is then repeated for each subsequent bit, with the end result of the ADC conversion being the setting of the DAC.

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The comparator compares the DAC output with the analog input.

That's how successive approximation ADCs work - they scan through one bit at a time, starting from the MSB, if the sampled voltage is more or less that the DAC output.

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