How it works
A Karnaugh map is a two-dimensional truth table arranged so that adjacent cells differ by exactly one variable (Gray code ordering). For a 3-variable map (8 cells), each cell represents one minterm. Groups of 1s (subcubes) must be powers of 2: groups of 1, 2, 4, or 8. Larger groups give simpler expressions — a group of 8 gives a constant 1. Cells on opposite edges wrap around and can form valid groups. The simplified SOP term for each group contains only the variables that remain constant within the group; variables that change are eliminated. Don't care conditions (marked X) can be included in groups to make them larger, but don't care output minterms need not be covered. For POS minimisation, group the 0s instead and complement the result.
Key points to remember
Grouping rules: groups must be rectangular or wrapping, sizes must be powers of 2, overlap between groups is allowed. Each 1 must be covered by at least one group; use the fewest and largest groups for the simplest expression. For four variables (16-cell map), the four corners form a valid group of 4. Don't cares can be treated as 1s when grouping (to enlarge groups) but never need to be covered alone. A prime implicant is the largest possible grouping of a given cell; an essential prime implicant is a group that covers at least one minterm covered by no other group. The Quine-McCluskey method is the tabular equivalent of K-map for more than 4 variables where visual grouping becomes error-prone.
Exam tip
Every Anna University digital electronics paper includes a 4-variable K-map minimisation problem — remember that the four corner cells (m0, m2, m8, m10) form a valid group, and mark this group first if all four are 1s or don't cares.