Karnaugh Maps
Boolean laws (like De Morgan's) work, are prone to human error. Enter the Karnaugh Map (K-map) : a visual tool that lets you simplify logic circuits by circling groups of 1s. What is a K-map? A K-map is a grid-based representation of a truth table. It organizes minterms in a way that adjacent cells only differ by one bit . This specific ordering is known as Gray Code . K-maps turns algebraic manipulation into a pattern-recognition game. They helps you see which variables are redundant. It's much harder to miss a term in a grid than in a long string of variables. Step 1: Map the Truth Table Transfer your output values (1s and 0s) from your truth table into the K-map grid. Pay close attention to the Gray code sequence (00, 01, 11, 10). The last two columns/rows are swapped. Step 2: Group the 1s Groups must contain 2^n cells (1, 2, 4, 8, or 16). Always aim for the largest possible group. Larger groups mean a simpler final expression. The K-map is spherical. The leftmost cells ...