Counter Power on Reset only

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I think, a power-up condition different from asynchronous reset doesn't make much sense. However, from hardware description, I expect that both options exist independantly.

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It depends on the device. In this case, Cyclone II, I know from experience that it is not possible. Power-up level must be the same as the async reset one. Quartus definitely issues a warning (or an error, I don't remember for sure) when the power-up and async reset levels are incompatible.