Analyze variables, prime implicants, coverage, and simplification tradeoffs. Compare original and minimized forms with charts. Build leaner circuits with clearer Boolean reasoning and documentation.
Use comma-separated values or ranges. Example: 0,1,2,5-7.
| Variables | Minterms | Don’t-cares | Simplified SOP | Why It Simplifies |
|---|---|---|---|---|
| A, B, C | 1, 3, 5, 7 | None | C | Every true row has C = 1, so other literals disappear. |
| A, B, C, D | 0, 2, 8, 10 | None | B'D' | Rows group across A and C, leaving only B' and D'. |
| A, B, C, D | 0, 1, 2, 5, 6, 7, 8, 9, 10, 14 | 3, 11, 15 | Tool generated | Don’t-care terms often create larger implicant groups and fewer literals. |
Canonical Sum of Products: F = Σm(minterms). Each minterm is converted into a product term using all variables. A binary 1 keeps the variable uncomplemented, while a binary 0 adds a complement.
Prime Implicant Generation: Terms differing in exactly one bit are merged. The differing bit becomes a dash, meaning that variable is no longer required in that implicant.
Selection Rule: Essential prime implicants are chosen first. Remaining uncovered minterms are then covered with the smallest term set, using literal count as the tie-breaker.
Reduction Metrics: Term Reduction % = ((Original Terms - Minimized Terms) / Original Terms) × 100 and Literal Reduction % = ((Original Literals - Minimized Literals) / Original Literals) × 100.
It converts minterm input into a canonical Boolean function, finds prime implicants, selects an efficient cover, and returns a minimized sum-of-products expression with metrics and tables.
Don’t-care states can be treated as either 0 or 1 during minimization. That flexibility often creates larger implicants, fewer terms, fewer literals, and simpler circuits.
A prime implicant is a merged product term that cannot be expanded further without covering unwanted zeros. It is a building block for minimized Boolean expressions.
An essential prime implicant covers at least one minterm that no other prime implicant covers. Those implicants must appear in every valid minimum cover.
This page focuses on algorithmic minimization rather than drawing a map. The output still mirrors the same grouping logic used in Karnaugh-map simplification.
The form supports up to six variables. That keeps the truth table readable and the minimization process fast enough for most educational and design use cases.
Some Boolean functions have limited adjacency, sparse true outputs, or constraints that prevent larger merges. In those cases, the minimized expression naturally remains multi-term.
Yes. The CSV is helpful for spreadsheets and audits, while the PDF captures the visual summary, expression, metrics, tables, and chart for documentation.
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.