E12 Sequential Systems and State Machines

Topic

Unlike a purely combinational circuit—whose output depends solely on its current inputs—a sequential circuit possesses memory: its output depends on both current inputs and an internal state stored from previous moments. The most basic memory element is the D flip-flop; the moment the system clock changes state, this element captures the value present at its input and holds it at its output until the next clock cycle.

For a synchronous circuit to operate reliably, a strict timing condition must be met: the signal must arrive and stabilize at each flip-flop's input well before the clock edge and remain stable for a brief moment after that edge. The time required for the signal to traverse the circuit's slowest logic path, combined with this stabilization margin, determines the maximum clock frequency at which the entire circuit can operate reliably.

Finite state machines provide the conceptual framework for modeling systems that transition between a limited number of discrete states based on received inputs; they form the foundation of virtually all digital control, ranging from communication protocols to peripheral controllers. Binary counters—composed of multiple cascaded flip-flops—divide a clock signal's frequency by successive powers of two, representing the simplest method for generating lower frequencies from a reference frequency.

Just as with the combinational logic described earlier, the dynamic power consumed by a sequential circuit increases linearly with its operating frequency and—even more rapidly—with its supply voltage.

Thus, this module—which began by distinguishing between outputs that depend on the past and those that do not—concludes by revisiting the same finding regarding energy consumption established by the combinational logic model: adding memory to a circuit does not alter the most effective lever for controlling its power consumption, which remains the supply voltage rather than the clock frequency.

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