I have a Carrier Infinity (with the ABCD Bus wiring system) that has died, and I want to replace it with another, standard thermostat. Is there a way to convert the ABCD to standard wiring? Thanks!

Carrier model #, inside unit?
Is the ABCD bus used on the outdoor unit?
Model # of the outdoor unit?
Your sure this isn't a heat pump?

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If the ABCD bus is used on the outdoor unit, you may have a problem making it work.

In general, Carrier provides the standard terminals on the control board, but to select a conventional stat, I believe the outdoor unit has to use C & Y, not 100% sure.

You would also need to know the stages of heat and the stages of cool to pick the right stat.

If you only have 4 wires, you may be relying on batteries if there are not enough wires run to support a common terminal.

No, that system is communicating and can't be used with a conventional stat as far I know.