Every example, every tool page, and every technique on this site — K-maps, Quine-McCluskey, Petrick's method — applies to one specific category of digital circuit: combinational logic. That's not a limitation to apologize for; it's a scope worth being explicit about, because the other category, sequential logic, needs genuinely different tools, and knowing the boundary saves you from reaching for a K-map on a problem it can't solve.
Combinational logic: output depends only on current inputs
A combinational circuit's output is a pure function of its current inputs, full stop — the same inputs always produce the same output, regardless of what happened a moment ago. A 7-segment decoder, an adder, a comparator, a parity checker — every example on this site — are all combinational. Feed in the same 4 bits twice, get the same result twice, with no dependency on history.
Sequential logic: output depends on history too
A sequential circuit's output depends on both the current inputs and some stored internal state — meaning the exact same inputs can produce different outputs depending on what happened before. A traffic light controller cycling through red-yellow-green, a counter, a vending machine's state logic — these all need to "remember" where they are, which means they need actual memory elements (flip-flops or latches) that a pure combinational circuit doesn't have.
The dividing line: memory
That's the entire distinction, reduced to one word: memory. No memory element anywhere in the circuit means it's combinational, full truth table, one row per input combination, done. Any memory element (even one flip-flop) means it's sequential, and a plain truth table can't capture it — the same input row can legitimately have different correct outputs depending on the current state, which a truth table has no way to express.
Why a K-map can't help with sequential logic
A K-map fundamentally assumes one output value per input combination — that's the entire premise a truth table (and everything built from it) depends on. Sequential logic breaks that premise directly: the same inputs can validly map to different outputs depending on state, which isn't a "big K-map" problem, it's a different kind of problem that needs a different kind of tool.
What sequential logic design actually uses instead
Sequential circuits are designed with state diagrams and state tables that explicitly track "current state + input → next state + output," then flip-flops (D, JK, or T type) to implement the memory itself. The combinational parts of a sequential circuit — the logic that computes the next state or the output from the current state and inputs — are still designed with the exact same K-map and Boolean algebra tools covered throughout this site. It's specifically the state-holding part that needs different techniques, not the whole circuit.
Quick test: which is it?
Ask one question: does the correct output ever depend on anything other than what the inputs are right now? If no, it's combinational — every tool and example on this site applies directly. If yes, the memory/state-holding part needs sequential design techniques, though any purely combinational sub-logic inside it (computing a next-state value, for instance) is still fair game for a K-map.
All combinational logic, verified and ready to use: browse the worked examples or open the K-map solver directly.