Simplify any boolean algebra expression or minterm list to its minimal Sum-of-Products and Product-of-Sums form. See prime implicants and every reduction step.
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The Boolean Algebra Simplifier reduces any two to four variable logic function to its minimal form. Enter a boolean expression such as A + B'C, or a list of minterms with optional don't-care terms, and see the minimized Sum-of-Products and Product-of-Sums results side by side.
Every prime implicant is listed with the terms it covers and whether it is essential, and the full Quine-McCluskey narration walks through each combination round. A read-only truth table shows the output for all input combinations.
Boolean algebra simplification rewrites a logic function as an equivalent expression with fewer terms and literals. A simpler expression needs fewer gates in the final circuit while producing the same output for every input.
Quine-McCluskey groups minterms by how many 1 bits they contain, repeatedly combines terms that differ in exactly one bit, and collects the terms that can no longer be combined as prime implicants. A coverage chart then selects the smallest set of prime implicants covering every minterm.
A prime implicant is essential when it is the only one covering some minterm, so it must appear in the minimal expression. Some functions have no essential prime implicants at all, which is a valid result rather than an error.
Don't-care terms are input combinations that never occur or whose output does not matter. Treating each one as 0 or 1, whichever helps, widens the search and often yields a noticeably smaller expression.
AND is juxtaposition (AB), an asterisk (A*B) or a dot (A.B); OR is a plus sign (A + B); NOT is a trailing apostrophe (A') or a leading exclamation mark (!A). Variables are named A, B, C and D in order, for two to four variables.
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