Analyze an existing synchronous circuit by deriving each flip-flop's next-state equation, deriving its output equation, and evaluating them for every state/input combination. Those values form a state table. A diagram then reveals the behavior encoded by the gates and storage elements.
Worked example
Suppose a one-bit circuit uses D = Q XOR X and output Y = Q. For Q = 0, X = 0 it stays zero; for 0,1 it becomes one. For 1,0 it stays one; for 1,1 it becomes zero. Thus X requests toggling and Y reports the current state.
What to watch for
Use old Q values when computing all next states for one clock edge. Updating one flip-flop before evaluating another incorrectly models sequential hardware as ordered software assignments.
Try it yourself
What happens if X stays one in this circuit?
Answer: Q toggles at every active edge, alternating zero and one, subject to valid timing.
How to study this topic
Begin with named states and a complete transition table. Then choose encodings and derive the logic. Trace inputs over several cycles, checking outputs as well as next states, including reset and unexpected encodings.
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Digital Electronics