Boolean Algebra Simplifier
Enter any boolean expression and simplify it to the minimal sum-of-products (SOP).
What it does: Simplifies a complex boolean expression down to the fewest product terms.
When to use it: Simplifying a logic circuit, reducing the gate count, or checking a hand simplification.
Simplify to the minimal sum-of-products (SOP)? , using Quine–McCluskey internally to find the prime implicants? .
MEANS Simplified to — product terms and — literals, using variables —.
No history yet. Each calculation is automatically saved to this device.
How to use the boolean algebra simplifier
Write an expression → simplify → read the minimal SOP.
- 01
Write a boolean expression
Use single letters A–Z for variables. Operators can be written as words
AND OR NOT XORor as symbols& | ! ^, and parentheses()change precedence. - 02
Click "Simplify" or compute as you type
The tool first expands the expression into a truth table, then uses the Quine–McCluskey + Petrick method to find the exact minimal form.
- 03
Read the minimal result
You get the minimal sum-of-products F = …. Expand "See how it was computed" to see which minterms each product term covers.
Operator notation reference
Both words and symbols are supported, and mixing them is fine (e.g. <code>(A|B) AND !C</code>).
| Operation | Word | Allowed symbols |
|---|---|---|
| NOT | NOT | ! ~ ¬ |
| AND | AND | & * · ∧ |
| OR | OR | | + ∨ |
| XOR | XOR | ^ ⊕ |
| Grouping | —— | ( ) |
Same safe parser as the truth table generator (no eval).
Common questions, answered in 3 minutes
How many variables are supported at most?
5 (any letters such as A–E), corresponding to a truth table of up to 32 rows, which keeps the minimization algorithm exactly solvable. With more variables, split into subexpressions and simplify each separately.
Is the result unique?
This tool gives one minimal sum-of-products (SOP) with the fewest literals/terms. If several optimal solutions tie, it picks one by a fixed rule, so the result is stable and consistent every time.
Can it output minimal product-of-sums (POS)?
Currently it only outputs minimal sum-of-products (SOP). If you need POS, simplify the negated output and then convert using De Morgan's laws.
Does it support NAND / NOR / XNOR?
These compound keywords are not supported yet; rewrite them in composed form, e.g. write NAND as NOT(A AND B).
How does it differ from the Karnaugh map solver?
The K-map tool starts from the cells you light up (minterms); this tool starts from the boolean expression you write, expanding it first and then simplifying — both use the same Quine–McCluskey engine.
Standards and sources referenced by this tool
| Item | Value / Formula | Source |
|---|---|---|
| Prime implicants | Quine–McCluskey | Quine 1952 / McCluskey 1956 |
| Minimal cover | Petrick's method | Petrick 1956 |
Pure algorithmic computation, no external API.