Karnaugh maps of k-maps are a useful visualization of truth tables. They are very useful for minimizing our logical circuit into a simpler gate logic representation.
We define regions within the k-map, where we have a value for a given variable:
| x y | 0 | 1 | | — | — | — | | 0 | x’y’ | x’y | | 1 | xy’ | xy |
The 0 and 1 in each row and column tell us the value of the variable, and the cells thus represent each minterm.
| x yz | 00 | 01 | 11 | 10 | | — | — | — | — | — | | 0 | x’y’z | x’y’z | x’yz | x’yz’ | | 1 | xy’z’ | xy’z | xyz | xyz’ |
The important property of the map useful to us is that adjacent squares in the map differ only by one variable, which is primed in one square and unprimed in the other. This allows us to do some very helpful logic gate minimizations.