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From the specified common mode range it should be possible to operate the AD7788/90 on Vdd = +5V as follows: REFIN- connected to GND, REFIN+ conneceted to VDD/2. AIN- is connected to GND, AIN+ is the input for a voltage derived from Vdd by a variable resistive divider, and is in the range of 0V...+5V. If the input overloaded? Do we have to expect restrictions on accuracy from the offset? If yes, by what degree and above/below of which limits?
The inputs of these devices are DIFFERENTIAL. If you ground AIN- then you can only use the positive half-scale at unity gain since AIN+ may not be more than 30mV below the negative rail - and Vin(max) will be +2.5 V and you will lose the lower half of the 5 V span. If you want a 0-5 V span you must bias AIN- to +2.5V and apply 0 - +5 V to AIN+. The offset of these devices is 3 uV so should not be a problem.