Advanced Boolean reduction for students, engineers, and designers. Enter variables, terms, modes, and don't cares. Review tables, download files, and verify minimized outcomes easily.
Boolean equation minimization converts a long canonical expression into a shorter logic form that preserves the same output behavior. This calculator works with minterms for sum-of-products reduction and maxterms for product-of-sums reduction. It also supports don't-care conditions, which can legally merge adjacent groups and reduce literal count further.
The tool is useful in mathematics, digital logic, switching theory, embedded design, and exam preparation. Instead of simplifying by hand every time, you can enter terms directly and obtain the reduced expression, truth table, prime implicants, and graph in one report. The result section appears above the form after submission so the final expression is immediately visible.
For advanced verification, the report includes the canonical definition, selected implicants, output states for every term, CSV export, and PDF export. This makes it practical for classroom review, homework checking, circuit drafting, and documentation. Because the table includes every input combination, you can confirm that the minimized result still matches the intended Boolean behavior.
SOP form: F(x) = Σm(terms)
POS form: F(x) = ΠM(terms)
The reduction engine applies Quine-McCluskey grouping. Terms that differ in exactly one bit are merged into a larger implicant. All non-combinable groups become prime implicants. Essential prime implicants are selected first. Any uncovered terms are then solved with a minimal cover search.
In SOP mode, a bit value of 1 keeps a direct literal and a bit value of 0 keeps a complemented literal. In POS mode, each selected implicant is converted into a sum factor. The final minimized answer is the shortest exact logical form found by the selection process.
| Variables | Mode | Target Terms | Don't Cares | Reduced Result |
|---|---|---|---|---|
| A, B, C | SOP | 1, 3, 5, 7 | None | C |
| A, B, C | SOP | 2, 3, 6, 7 | None | B |
| A, B | POS | 0 | None | (A + B) |
| A, B, C, D | SOP | 0, 2, 8, 10 | None | B' · D' |
It reduces canonical Boolean definitions into shorter SOP or POS expressions. The tool uses minterms, maxterms, don't cares, prime implicants, and exact cover selection to produce a compact final form.
Choose SOP when you know the input combinations where the function equals 1. Enter those minterms, add optional don't-cares, and the calculator returns a reduced sum-of-products expression.
Choose POS when you know the combinations where the function equals 0. Enter those maxterms, and the calculator converts the reduced coverage into a product-of-sums result.
Don't-care terms are unused or irrelevant states. They may be grouped during minimization to shrink the final expression, but they are not forced to appear as fixed 1 or 0 outputs.
This page supports two to six variables. That range keeps the exact minimization process practical while still covering many academic and engineering Boolean reduction exercises.
The page places the output directly below the header and above the form after submission. This layout keeps the reduced expression visible first, then lets you adjust inputs underneath.
The Plotly chart shows each indexed term and its state. Standard outputs appear as 0 or 1, while don't-care conditions are marked separately for quick visual inspection.
Yes. Use the CSV button for spreadsheet-ready output and the PDF button for a saved report. The page also includes a print option for paper or browser-based PDF generation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.