LOGIC MINIMIZER & K-MAP
Type an expression or click the map. Quine–McCluskey finds every prime implicant, then a branch-and-bound exact cover picks a provably minimal one — fewest terms first, then fewest literals. Not a greedy guess.
Single letters are variables (so AB means A AND B).
' ! ~ negate, & * ·
are AND, + | are OR, ^ is XOR, and
AND OR NOT XOR NAND NOR XNOR work as words. Constants 0 and 1 too.
Click a Karnaugh cell to cycle it 0 → 1 → X. X is a don't-care: the
minimiser may use it or ignore it, whichever makes the result smaller.
Cells are Gray-coded, so neighbours — including across an edge — differ in one variable.
Every implicant that cannot be widened further. Essential ones cover a 1 no other implicant reaches, so they are in every minimal cover; chosen marks the rest of the cover picked here. Hover or tap one to light it up on the map.
Gate counts assume a two-level implementation with unlimited fan-in, and count an inverter per complemented literal once (not once per use). NAND-only and NOR-only forms follow from the two De Morgan identities and always use the same number of gates as the AND-OR form they come from.
"The map is the proof: every result is re-checked against all 2^n rows before it reaches the screen."