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How do digital inputs work?

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How does a digital input work?

 

I suspect that it's a flip-flop with a clock input, so that the value of the digital input is sampled at the rising (or falling) edge of the clock.

I see a problem with this though. If I wanted the digital input to be a counter, then, if the input is another clock running faster than the system (sampling) clock, I would not be able to count accurately.

So how are digital inputs usually implemented?

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