Every minimal SOP or POS expression this solver produces is a two-level circuit — one layer of AND gates (or OR gates, for POS) feeding a single final gate. That's not the only way to build a circuit, though, and knowing when a deeper, multi-level design actually wins is worth understanding even though it's a different optimization goal than what K-map minimization targets.
What two-level logic is
Exactly what "minimal SOP" means structurally: every input signal passes through exactly one gate (an AND, for SOP) before reaching a second and final gate (the OR combining all the AND outputs). Two layers, full stop — which is precisely why K-map minimization, Quine-McCluskey, and this site's solver all optimize for two-level literal and term count. It's also the fastest possible structure in terms of propagation delay, since a signal only ever passes through two gates before reaching the output.
What multi-level logic is
Factoring an expression algebraically (exactly the technique in Algebraic Boolean Simplification Without a K-Map) can restructure it into more than two gate layers, often using fewer total gates or literal connections in exchange for a signal passing through more gates before reaching the output.
A worked comparison
Take the majority function F = AB + AC + BC — the minimal two-level SOP, verified in Overlapping Groups in K-Maps. As a two-level circuit: 3 AND gates plus 1 OR gate, 4 gates total, 6 literal connections (2 per AND gate × 3), 2 gate layers deep.
Factored differently: F = A(B+C) + BC — verified equivalent by truth table. As a circuit: an OR gate for (B+C), an AND gate combining that with A, a separate AND gate for BC, and a final OR combining both results. Still 4 gates total, but only 5 literal connections instead of 6, at the cost of 3 gate layers deep instead of 2 — a signal through the A(B+C) path now passes through three gates before reaching the output, not two.
The actual trade-off
Two-level logic is faster (fewer gate delays between input and output) and is exactly what K-map and Quine-McCluskey minimization are built to produce. Multi-level factoring can reduce total gate count or literal connections — which matters for chip area and power — at the direct cost of propagation delay, since more gate layers means a longer worst-case path from input to output. Neither is universally "better"; which one wins depends on whether the design priority is speed or size.
Where this fits with the rest of this site
Every expression and circuit diagram this solver generates is the two-level form, by design — it's what K-map minimization is actually solving for. If a specific problem calls for a multi-level, gate-count-optimized result instead, that's the algebraic factoring technique covered in Algebraic Boolean Simplification Without a K-Map, applied as a separate step after minimization rather than something the solver does automatically.