Logic Lab
Canonical Forms
Turn any expression into a truth table, minterms and maxterms, canonical and standard SOP and POS.
Boolean expression analyser, up to 8 variables
Letters A–Z, 0/1, NOT as ! ~ or ′, AND as & * · or by writing terms together, OR as | or +, XOR as ^.
Simplified forms
Circuits made from logic gates
AND gates feed one OR gate. A circle on a gate input is an inverter, so there is one gate per term plus the final gate. Flip the inputs to check the answer.
OR gates feed one AND gate. A circle on a gate input is an inverter, so there is one gate per term plus the final gate. Flip the inputs to check the answer.
Properties
Try it live
Compare with another expression
Truth table
| # | A | B | C | F |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 1 | 1 |
| 2 | 0 | 1 | 0 | 1 |
| 3 | 0 | 1 | 1 | 1 |
| 4 | 1 | 0 | 0 | 1 |
| 5 | 1 | 0 | 1 | 1 |
| 6 | 1 | 1 | 0 | 0 |
| 7 | 1 | 1 | 1 | 1 |
The first variable is the most significant bit. Simplification uses the same Quine–McCluskey engine as the Logic Solver, with an exact minimum cover. NAND–NAND and NOR–NOR show how the minimal forms map onto a single gate type, which is how many real chips are built. Self-dual means F(x) = ¬F(¬x); monotone means turning an input from 0 to 1 never turns F from 1 to 0.