State Diagrams

A state diagram is a picture of an FSM. Circles are states, arrows are transitions, and the label on each arrow is the input condition that has to be true for that transition to happen.

Reading one arrow tells you everything it describes: the state it leaves, the condition on its label, and the state it points to. An arrow from S0 labeled w=1 pointing to S1 means "while in S0, if the input w is 1, move to S1." An arrow that loops from a state back to itself, labeled w=0, means "while in this state, if w is 0, stay here."

Every state diagram needs a reset state — the state the circuit starts in every time, regardless of what happened before power-on. Without one, the circuit's starting condition would depend on chance, the same problem an un-reset flip-flop has in simulation. A reset arrow, usually drawn from outside the diagram, marks which state that is.

A transition that is not drawn simply does not happen. If no arrow connects two particular states under a particular input condition, the diagram is telling you that move never occurs — the hardware built from this diagram will never make that jump. This is why reading a state diagram carefully matters: what is missing is just as meaningful as what is there.

Once a state diagram is complete, it can always be converted to an equivalent state table — one row per (current state, input) pair, listing the next state. The table and the diagram carry exactly the same information in two different representations; some people find one easier to design from and the other easier to verify against.