Sequential Logic and State

Circuits That Remember

Combinational circuits are memoryless, but a computer must remember. Sequential logic adds state, meaning the circuit's output depends on current inputs and stored past information.

Memory comes from feedback, wiring an output back to an input. A latch is the simplest memory element, storing one bit that can be set to 1 or reset to 0.

Real designs are synchronous, governed by a clock ticking at a fixed rate. State updates happen only at a clock edge (rising or falling transition).

Finite State Machines

A finite state machine (FSM) consists of a set of states, plus rules to determine the next state and outputs. Examples include traffic lights and CPUs.

$$\text{next state} = f(\text{state}, \text{input})$$

Here, $\text{state}$ is held by the state register, while combinational logic computes the next state.

Common pitfall: Thinking a sequential circuit responds continuously. In synchronous designs, state changes only at clock edges, advancing one step per tick.