Truth Table to Expression Converter

Click your truth table's outputs, get the Boolean expression

Build your truth table

Variables: Click output cells to toggle 0 / 1

How to use ?

  • Choose 2, 3 or 4 variables.
  • Click the output cells to toggle them between 0 and 1 — or try a preset.
  • Click "Generate Expression".
  • Get minterms, maxterms, canonical SOP/POS and the minimized form — then copy the share link.

Minterms & Maxterms

A minterm is an AND-term that is 1 for exactly one truth-table row. The list of 1-rows, written Σm(...), is the canonical Sum of Products (SOP): OR all the minterms together. A maxterm is an OR-term that is 0 for exactly one row; the 0-rows, written ΠM(...), give the canonical Product of Sums (POS): AND all the maxterms together. Both forms describe the same function — the minimized SOP is the shortest equivalent form.

From Truth Table to Expression — FAQ

How do I read Σm(1, 2, 4)? It lists the minterms — the row numbers (in binary counting order, starting at 0) where the output is 1. Σm(1, 2, 4) means rows 1, 2 and 4 output 1.

When do I use SOP vs POS? Use SOP when the table has few 1s (fewer minterms to OR); use POS when it has few 0s (fewer maxterms to AND). Both are always correct.

What does "minimized" mean? The shortest expression with the same truth table, found here with the Quine–McCluskey algorithm — fewer gates if you build the circuit.

Can I share my table? Yes — after generating, the page URL encodes your table (e.g. ?vars=2&out=0110). Copy the link and anyone opening it sees your exact table and results.