Karnaugh Map (K-Map) Solver

Simplify Boolean expressions using Karnaugh maps. Enter a Boolean expression or truth table values to get the minimized SOP or POS form.

Use: ' for NOT, + for OR, * or nothing for AND. Example: A'B + AB'
Common formats: A'B'C + A'BC + ABC' + ABC, (A+B)(A+C), etc.

Simplified Expression

-
POS Form: -

K-Map Result

Step-by-Step Solution

Enter a Boolean expression or truth table values, then click "Simplify Expression" to see the step-by-step solution.

What is a Karnaugh Map?

A Karnaugh Map (K-Map) is a graphical method for simplifying Boolean algebra expressions. It arranges truth table values in a grid where adjacent cells differ by only one variable, making it easy to identify and eliminate redundant terms.

How to Use

  • 2 Variables: 2x2 grid (4 cells)
  • 3 Variables: 2x4 grid (8 cells)
  • 4 Variables: 4x4 grid (16 cells)
  • Group adjacent 1's in powers of 2 (1, 2, 4, 8, 16)
  • Larger groups = simpler expression

Boolean Algebra Rules

  • Consensus: AB + AC + BC = AB + AC
  • Absorption: A + AB = A
  • DeMorgan's: (A+B)' = A'B'
  • Distributive: A(B+C) = AB + AC

Karnaugh Map Solver: Complete Guide to Boolean Expression Simplification

What is a Karnaugh Map? A Karnaugh Map (K-Map) is a visual method for simplifying Boolean algebra expressions. It was invented by Maurice Karnaugh in 1953 and is widely used in digital logic design to minimize logic gates in circuits.

How K-Map Simplification Works: The K-Map arranges truth table values in a grid where adjacent cells differ by only one variable. By grouping adjacent 1's in powers of 2 (1, 2, 4, 8, 16 cells), you can identify and eliminate redundant variables, resulting in the simplest possible Boolean expression.

Common K-Map Sizes:

Pro Tip: Always circle the largest possible groups of 1's first. Groups can wrap around the edges of the K-Map (toroidal topology). Don't forget to include don't care conditions (X) as 1's when they help create larger groups!