Boolean Minimization Lab
Specify each truth-table row as 0, 1 or X, or enter ON and don't-care minterm lists. This lab combines implicants with Quine–McCluskey and searches exact covers within a four-variable limit. It first minimizes the number of SOP terms, then the number of literals, and retains all equally minimal covers. Every expression is checked against all specified 0 and 1 rows; X rows may take either output.
Key features
- 2–4 named Boolean inputs with editable truth-table rows and minterm ranges
- Strict detection of duplicate, overlapping and out-of-range indices
- Exact Quine–McCluskey prime implicants and minimum cover by term count, then literal count
- All tied optimum expressions and exhaustive verification on every specified input
- Gray-ordered Karnaugh map with selected implicant group labels and standalone SVG
- Download expression text, all-solution JSON and selected Karnaugh SVG
How to use
- Choose two to four inputs and mark each truth-table row 0, 1 or X; alternatively type comma-separated ON and don't-care indices or short ranges.
- Apply list edits or press Minimize. A changed table updates the lists automatically.
- Read the verified SOP and select among equal optima when more than one exists.
- Inspect Gray-ordered map cells and group labels, including groups that wrap around map edges.
- Download the expression, machine-readable result JSON or a standalone Karnaugh SVG.
Use cases
- Find a compact combinational SOP from a small specification
- Compare equally minimal covers before drawing a gate circuit
- Teach prime implicants, don't-cares and wraparound Karnaugh groups
- Check a manually simplified expression against every specified truth row
Frequently asked questions
What does X mean?
X is a don't-care input. The minimized output can be 0 or 1 at that row; only specified 0 and 1 rows must match. Do not mark a required behavior X.
What does minimum mean here?
Among sum-of-products covers, the lab minimizes the number of product terms first and the total number of literals second. It lists every cover tied on both measures; it does not optimize gate-library delay or power.
Is the result exact?
Yes for the supported 2–4 variables and this SOP objective. Quine–McCluskey derives prime implicants, exact cover search finds all optima, and every non-X truth-table row is exhaustively checked.
Why can one group appear on opposite map edges?
Karnaugh rows and columns use Gray order. The first and last cell in a row or column are adjacent by one input bit, so a valid implicant may wrap across the drawn edge.
Does this simulate a real circuit?
No. It minimizes a static combinational truth table. It does not model propagation delay, flip-flop state, hazards or physical gate cost.
Are my inputs uploaded?
No. Editing, minimization and downloads run in this browser tab.
Privacy
Truth tables and expressions stay in this browser tab; no server-side computation or upload is used.
Comments & questions