How to use it
- Type the expression. With single-letter variables you can write it the way textbooks do:
A'B + AB',(A + B)(A + C). - Optionally list don’t-care minterms.
- Read the minimal sum of products and product of sums, and check the Karnaugh map.
How it works
The tool builds the truth table with the variables in alphabetical order (the first is the highest bit of the minterm number). The Quine–McCluskey method merges minterms that differ in one variable until no more merges are possible; what is left are the prime implicants. A branch-and-bound search then picks the cheapest set of primes that covers every minterm, counting terms first and literals second. For the product of sums the same is done for the zeros of the function, and each term is complemented.
Worked example
AB + A’C + BC is 1 for the minterms 1, 3, 6 and 7. The primes are A’C (1, 3), BC (3, 7) and AB (6, 7). Minterm 1 needs A’C and minterm 6 needs AB; together they also cover 3 and 7, so BC is redundant: the minimal form is AB + A’C (the consensus theorem). The zeros 0, 2, 4, 5 give the product of sums (A + C)(A’ + B).
Tips
- Use brackets when mixing AND and OR: NOT binds tightest, then AND, then XOR, then OR.
- An expression that simplifies to 1 is a tautology; one that simplifies to 0 can never be true.
- To see every row, paste the expression into the truth table generator.