Karnaugh Map Solver
Simplify boolean expressions instantly with a visual, step-by-step Karnaugh Map solver.
Also accepts !, *, AND/OR/NOT, and implicit AND (e.g. AB'C).
Result
Sum of Products (SOP)
F = 0
- Terms
- 0
- Literals
- 0
- Gates
- 0
Circuit diagram
Step-by-step
1Read the map▾
Collected the entries from the 4-variable K-Map.
- Minterms (1s): none
- Maxterms (0s): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
- Don't-cares (X): none
2Constant function▾
There are no 1-cells, so the function is always 0 (don't-cares can be assigned 0).
- F = 0
How it works
From a boolean function to a minimized, gate-level circuit in four steps.
Choose your variables
Pick 2, 3, 4, or 5 variables to match the boolean function you're minimizing.
Enter your function
Type a boolean expression, list minterms or maxterms, or fill in the truth table directly.
Read the grouped map
Pairs, quads, and octets are outlined automatically as the solver finds the largest valid groups.
Get the minimized result
Copy the simplified SOP or POS expression, view the gate-level circuit, or export a PDF.
What you'll see
A preview of the tool's main views. Scroll to browse.
Frequently asked questions
A Karnaugh Map (K-Map) is a visual tool for simplifying boolean expressions. Instead of manually applying boolean algebra laws, you place 1s, 0s, and don't-cares on a gray-code grid and group adjacent cells to read off a minimized sum-of-products or product-of-sums expression.
The solver supports 2, 3, 4, and 5 variable functions. Five-variable maps are shown as two side-by-side 4-variable planes, which is the standard way to extend a K-Map beyond four variables.
Don't-cares (X) are input combinations where the output doesn't matter. The solver uses them to help form larger groups when it's beneficial, but never treats a don't-care as required coverage — a group is only considered essential if it's the sole coverage for an actual required minterm.
Petrick's Method is used when a prime implicant chart is cyclic, meaning no group is the essential, unique choice for covering some minterm. It systematically multiplies out every valid way to complete the cover and selects the cheapest option by term count, then literal count.
Yes. Once you've entered a function, the results panel lets you download a PDF containing your input summary, the minimized expression, and the full step-by-step simplification trace.
Sum-of-products (SOP) groups the 1-cells and joins the resulting product terms with OR. Product-of-sums (POS) groups the 0-cells instead and joins the resulting sum terms with AND, using De Morgan's theorem on each term. Neither form is always shorter — it depends on the function.