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

  1. Groups must contain 2^n cells (1, 2, 4, 8, or 16).

  2. Always aim for the largest possible group. Larger groups mean a simpler final expression.

  3. The K-map is spherical. The leftmost cells are adjacent to the rightmost, and the top is adjacent to the bottom.

  4. You can use the same "1" in multiple groups if it helps you create a larger group elsewhere.

Step 3: Extract the Simplified Expression

  • If a variable changes (e.g., goes from 0 to 1) within the group, discard it.

  • If a variable remains the same, keep it.



~ Pritha Aggarwal       


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