Where unreachable states come from

Reachable states are the codes the reset state can walk to along defined arcs. Every other code the flops can hold is unreachable in normal operation.

Three sources produce them: codes the encoding never assigns, power-up values before reset asserts, and single-event upsets that flip a state bit. Synthesis may also trim logic for codes it proves unreachable, which changes nothing functionally but removes any accidental safety net.

Counting invalid codes

Invalid codes are the bit patterns with no state assigned. Fewer state bits mean fewer places to hide; one-hot pays for its speed with many invalid codes.

4 states in 2 bits (binary):   2^2 - 4 = 4 - 4 = 0 invalid codes
4 states in 4 bits (one-hot): 2^4 - 4 = 16 - 4 = 12 invalid codes
5 states in 3 bits (binary):   2^3 - 5 = 8 - 5 = 3 invalid codes

Three recovery techniques

Every technique steers invalid codes back to a safe state, usually the reset state. They differ in what they cost and what faults they catch.

The sketch below is illustrative and does not run: it shows the default-arc pattern used through this topic.

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// not-run: illustrative sketch, no testbench in this lesson
always_comb begin
  next = state;
  case (state)
    IDLE: if (go) next = WORK;
    WORK: if (fin) next = DONE;
    DONE: next = IDLE;
    default: next = IDLE; // every invalid code recovers
  endcase
end

Common mistakes

Reset alone is not recovery: it fixes power-up but never fires on an in-flight upset. Recovery must live in the next-state logic so it acts every cycle.

Related topics

• Up: FSM Synthesis

• Next: Output registering

• Flops, Resets and Enables