Build Karnaugh maps, draw groupings, and extract minimised SOP and POS expressions
A Karnaugh map (K-map) arranges truth table outputs so that logically adjacent cells differ by exactly one variable. Grouping adjacent 1s visually cancels variables and produces a minimal Sum of Products (SOP) expression.
Groups must contain 1, 2, 4, or 8 cells (powers of 2). Groups wrap around edges. Always use the largest possible groups. Don't-care (×) cells can be included to maximise group size.
SOP groups the 1s → AND terms ORed together → NAND-NAND implementation. POS groups the 0s → OR terms ANDed together → NOR-NOR implementation. Choose whichever produces fewer terms.