# Karnaugh diagramm online dating

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This image actually shows two Karnaugh maps: for the function ƒ, using minterms (colored rectangles) and for its complement, using maxterms (gray rectangles).

In the image, E() signifies a sum of minterms, denoted in the article as It also permits the rapid identification and elimination of potential race conditions.

The required Boolean results are transferred from a truth table onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in Gray code, and each cell position represents one combination of input conditions, while each cell value represents the corresponding output value.

Optimal groups of 1s or 0s are identified, which represent the terms of a canonical form of the logic in the original truth table.

Cells on the extreme right are actually 'adjacent' to those on the far left, in the sense that the corresponding input values only differ by one bit; similarly, so are those at the very top and those at the bottom. The K-map for the function f(A, B, C, D) is shown as colored rectangles which correspond to minterms.

The brown region is an overlap of the red 2×2 square and the green 4×1 rectangle.

These terms can be used to write a minimal Boolean expression representing the required logic.    They are usually indicated on the map with a dash or X.

For the red grouping: It would also have been possible to derive this simplification by carefully applying the axioms of boolean algebra, but the time it takes to do that grows exponentially with the number of terms.

The inverse of a function is solved in the same way by grouping the 0s instead.

The K-map for the inverse of f is shown as gray rectangles, which correspond to maxterms.

Once the Karnaugh map has been constructed and the adjacent 1s linked by rectangular and square boxes, the algebraic minterms can be found by examining which variables stay the same within each box.