Boolean Algebra Simplifier
Reduce a boolean function to its simplest Sum of Products and Product of Sums. Type an expression like A'B + AB', or enter the minterms (and any don't cares) over up to 8 variables, and the Quine-McCluskey method finds the prime implicants and a minimum cover.
How to simplify a boolean expression
- Choose an input mode: a boolean expression, or a list of minterms.
- For expressions, use single-letter variables with ' or ! for NOT, + for OR and juxtaposition or * for AND.
- For minterms, set the variable count and list the indices where the output is 1, plus any don't-care terms.
- Read the minimal SOP and POS forms, the prime implicants and which ones are essential.
Examples
Redundant expression
A'B + AB
Simplifies to B (the A term is redundant).
Minterms with the variable list
3 variables, minterms 1, 3, 5, 7
Simplifies to C, since every listed minterm has C = 1.
Frequently asked questions
What is the Quine-McCluskey method?
It is a tabular algorithm for minimizing boolean functions. It merges minterms that differ in a single bit to find all prime implicants, then selects a minimum set of them that covers every required minterm. Unlike a Karnaugh map it works the same way for any number of variables.
What input does the simplifier accept?
Either a boolean expression with single-letter variables, or a list of minterm indices over a chosen number of variables. With minterms you can also list don't-care terms, which the algorithm uses to simplify further when it helps.
Which operators can I use in an expression?
NOT is ', ! or ~ (postfix apostrophe like A' also works). AND is juxtaposition (AB), * or &. OR is + or |. XOR is ^. You can group with parentheses and use the constants 0 and 1.
What are prime implicants and essential prime implicants?
A prime implicant is a product term that cannot be combined into a larger one. An essential prime implicant is the only one that covers some minterm, so it must appear in every minimal solution. The tool lists both.
What is the difference between SOP and POS?
Sum of Products is an OR of AND terms, like AB + C'. Product of Sums is an AND of OR terms, like (A + B)(B + C). The tool gives the minimal form of each by minimizing the ones for SOP and the zeros for POS.
How many variables are supported?
Up to 8 variables (256 rows). Beyond that the prime-implicant chart can grow very large, so the tool reports an error instead of running indefinitely.
Is my expression sent to a server?
No. Parsing and minimization run entirely in your browser, so nothing you enter is uploaded or stored.
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