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From my understanding, combinational logic is dependent solely on input, and sequential logic involves state--memory.

When explaining a finite state machine (FSM), however, it is said that an FSM has two combinational functions. However, they both seem to involve memory, in that state is one of two inputs to the function.

Is there something that I am not grasping here?

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Combinational logic can (and frequently does) receive the output of memory on its inputs, or have its outputs stored in memory. It just doesn't have memory within itself.

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