sequential logic

Sequential logic is a class of digital circuits in which the output at any moment depends not only on the inputs present right now, but also on the states the circuit has passed through. Unlike combinatorial logic, which produces outputs instantly from inputs alone, sequential logic uses memory elements such as flip-flops or latches to retain information about previous conditions. This memory is what makes the circuit's behavior depend on its history.

The core of any sequential circuit is the clock signal, a regular pulse that synchronizes state changes across the system. On each clock edge (rising or falling, depending on the design), flip-flops sample their inputs and update their stored state. This is called synchronous sequential logic, the most common type in modern digital systems. Asynchronous sequential logic exists but is harder to design reliably because state changes can occur at any instant; it is used mainly where a clock signal is impractical or where speed is critical and margins are carefully managed.

Flip-flops and state machines

The fundamental building blocks are flip-flops: bistable devices with two stable states, typically labeled 0 and 1. Common types include SR (set-reset), JK, D (data), and T (toggle) flip-flops, each with different input behaviors. Flip-flops are cascaded and interconnected to form finite state machines, which move from one well-defined state to another based on input conditions and the clock. A simple example is a counter: its output increments on each clock pulse, storing the result in flip-flops. A more complex example is a sequencer that steps through a predetermined sequence of operations.

Sequential circuits are essential wherever order, timing, or state persistence matters: in microprocessors, control systems, communication protocols, and any digital system that must process information over time rather than instantaneously. Design requires careful attention to setup and hold times (the window during which an input must be stable relative to the clock edge), clock distribution, and the risk of metastability, which occurs when a flip-flop is disturbed near a clock transition and takes an unpredictable time to settle.

The contrast with combinatorial logic is sharp: a multiplexer or adder (combinatorial) responds to inputs within nanoseconds with no memory; a state machine (sequential) remembers its path through a sequence and produces outputs that encode not just the current input but the accumulated history. This distinction shapes how engineers partition any digital design: some blocks are pure logic, others stateful, and the interaction between them must be timed carefully to ensure correct operation across all temperature and voltage corners.