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The output from the AD7811 is stuck at 1023 decimal regardless of the voltages applied to the inputs.
The problem is to do with the way the AD7811 resets itself during power on. If Vdd drops down to the region 0.8-1.2V and is then brought back up again, the part is not able to reset itself properly and the device will lock up and only output the last converted code. The solution is to ensure that Vdd drops all the way to 0V when the power supply is cycled. There are number of ways in which this can be achieved. The simplest is to add a resistor across the power supplies but this obviously increases the power supply of the circuit as a whole. A FET current source across the power supplies can also be used to discharge the large capacitors which are used for power supply decoupling.