Analog differential input - how to make it measure 0V when floating

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esm.

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Hello.
I am using an external ADC (MCP3421), 16-bit resolution, with internal PGA (internal gain) of 8x to read signals from a thermocouple type T. Within my current ADC configuration, the differential input impedance is around 280K.
But when the inputs are floating, the result of ADC conversions behaves incorrectly (negative and positive aleatory values, sometimes with high values are read from ADC).

I want this ADC to output conversion values near to zero when the inputs are floating, to detect a sensor fault, or sensor disconnected, for example.

How could I do a "pull down" to it? because the Vin- input (reference) and Vin+ input (input signal) from the ADC and and the digital ground of the IC are not in the same voltage reference.
 

Pull the inputs to ground with 10kohm resistors
 

Is it OK to short the inputs togather.
 

No, pull each input down to ground with its own resistor
 

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