stateencoding

State encoding is the method used to represent the finite set of states in a finite state machine (FSM) with binary vectors or bit patterns. It is a key consideration in digital design, simulation, and modeling, because the chosen encoding affects hardware resources, timing, and power consumption as the machine transitions between states.

Common state encoding schemes include binary encoding, one-hot encoding, Gray code, and variants such as Johnson and ring encodings. Binary encoding assigns the smallest number of flip-flops necessary to represent all states, minimizing area but often requiring more complex combinational logic for next-state and output functions. One-hot encoding uses as many flip-flops as there are states, with exactly one bit high at any time; this simplifies the next-state logic and can yield faster, more robust designs at the expense of additional flip-flops. Gray code encodes states so that consecutive states differ by only one bit, reducing glitches and potentially lowering switching activity. Johnson and ring encodings provide alternative trade-offs between logic complexity and transition density, and may be chosen for specific timing or power goals.

The encoding choice influences synthesis results, including gate count, critical path, and dynamic power from state toggling. If an encoding is not chosen carefully, illegal or unreachable states can arise, complicating verification and reliability. In software and formal methods, states can be mapped to integers or enums, while in model checking, the encoding impacts state space size and memory usage; symbolic methods or BDDs are often used to mitigate state explosion.

Example: with four states, binary encoding uses two bits (00, 01, 10, 11); one-hot encoding uses four bits with a single high bit for each state.