Karnaugh map solver

Type the function as an expression, such as `AB + A'C`. If you have minterms instead, write each as a product: minterm 5 of three variables is 101, so it's `AB'C`. The map is drawn for two, three or four variables, with each group ringed in its own colour and the matching terms in the simplified answer.

The small number in each cell is its minterm number, so you can check the layout against your worksheet. Rows and columns run 00, 01, 11, 10, Gray code order, so neighbouring cells differ in one variable, edges included. A group that wraps from one edge to the other is drawn as its pieces, which is why the sample's corner group shows as four rings.

Ring the 1s in rectangles of 1, 2, 4, 8 or 16 cells, as large as possible, with the map treated as wrapping round at the edges. Each ring is one term: the variables that stay the same across it, and the ones that change drop out. Use as few rings as you can, overlapping is fine, and every 1 must be in at least one. A ring of two removes one variable, four removes two, eight removes three.

The solver finds the same answer with the Quine–McCluskey method, which follows the same rules without needing to see the shape. That's also what works past four variables, where maps stop being readable.

Maurice Karnaugh published the map in November 1953, in a paper titled The Map Method for Synthesis of Combinational Logic Circuits. It refined a chart Edward Veitch had published in 1952, and Veitch's chart turned out to repeat a logical diagram Allan Marquand drew in 1881. Karnaugh's change was the Gray code ordering, which puts cells that differ in one variable next to each other so groups can be seen at a glance. Two years later, in 1956, Edward McCluskey extended Willard Quine's 1952 method into the tabular one this solver uses.

Type it the way your course writes it. AND can be `·`, `*`, `&`, `&&`, `∧` or the word AND, or nothing at all, so `AB` and `A(B + C)` are ANDs. OR is `+`, `|`, `||`, `∨` or OR. NOT is a `'` after a term, as in `A'` or `(A + B)'`, or `!`, `~`, `¬` or NOT before it. XOR is `^`, `⊕` or XOR, and NAND, NOR and XNOR work as words. `0` and `1` are constants.

Single letters are variables, so `abc` means a AND b AND c. A name with a digit, mixed case or more than four letters stays whole, so `x1`, `Rain` and `sprinkler` each count as one variable. Up to eight variables fit, a table of 256 rows.