Boolean algebra simplifier — every law named, cross-checked two other ways.
Enter an expression and LogicBench simplifies it algebraically, naming the exact law applied at each step — De Morgan's, absorption, distribution, consensus, and the rest.
Where a K-Map or Quine-McCluskey give you a minimized result, this tool shows the algebraic proof — the specific sequence of identities that gets you there, which is what most DLD courses actually ask you to demonstrate on paper. Because it runs on the same expression as the rest of the suite, you get a second and third confirmation for free: the K-Map grouping and the Quine-McCluskey tabulation should land on the same minimized form through completely different methods, so if your hand-worked proof disagrees with one but not the others, you know exactly where to look.
4 steps, no signup.
Enter an expression
Type any Boolean expression, including nested NOT, AND, OR, XOR terms.
Step through the proof
Each simplification step names the exact Boolean law used to reach it.
Cross-check two other ways
Compare the algebraic result against the same expression's K-Map grouping and Quine-McCluskey tabulation.
Verify with a truth table
Cross-check the simplified expression against its truth table to confirm equivalence.
Solve it here, then wire it for real.
Every result in the Digital Logic Suite can be built directly in LogicBench’s simulator with real 74-series ICs — no retyping equations, no redrawing circuits by hand.
FAQ
What Boolean algebra laws does this tool use?
The standard identities used in digital logic simplification — De Morgan's theorem, absorption, distribution, idempotent and complement laws, and consensus — naming the exact law used at each step.
Is algebraic simplification the same as a K-Map?
They reach the same minimized result through different methods — a K-Map groups terms visually, algebraic simplification applies Boolean identities step by step, and Quine-McCluskey tabulates it a third way. All three run on the same expression in this suite, so they act as a check on each other.
Can I check my own hand-worked simplification against this tool?
Yes — enter your original expression and compare the tool's step-by-step result, plus its K-Map and Quine-McCluskey cross-checks, against your own working to see exactly where, if anywhere, they diverge.
The rest of the Digital Logic Suite.
K-Map Solver
Click cells or type an expression — get the minimized SOP, the algebraic proof, Quine-McCluskey steps, a truth table, a waveform, and a real gate-level circuit you can build with one click.
Circuit Diagram
The unsimplified and minimized gate-level schematics side by side, with exact term and gate counts — and a Build button that wires either one from real ICs in the simulator.
Truth Table Generator
The full truth table and a synced timing waveform, generated from the same expression as your K-Map, circuit, and Quine-McCluskey steps — no retyping between tools.