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From the state transition table below, how do I know if I'm constructing circuits for a Mealy or a Moore machine? Could someone explain the difference and what I should be looking for?

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The output Z is determined solely by the state and not the inputs. Therefore the machine is a Moore machine.

From Wikipedia:

...a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs.

(source)

..a Moore machine is a finite-state machine whose output values are determined only by its current state.

(source)

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