Using Boolean algebra to simplify Boolean expressions can be difficult and may lead to solutions which, though they appear minimal, are not. The Karnaugh map provides a simple and straight-forward method of minimising boolean expressions which represent combinational logic circuits. A Karnaugh map is a pictorial method of grouping together expressions with common factors and then eliminating unwanted variables.
A Karnaugh map is a two-dimensional truth-table. Note that the squares are numbered so that the binary representations for the numbers of two adjacent squares differ in exactly one position.
Rules for Grouping together adjacent cells containing 1's
Obtaining Product Terms
Karnaugh Maps are used to solve the following type of problem.
Bank Alarm System
A bank wants to install an alarm system with 3 movement sensors.
To prevent false alarms produced by a single sensor activation, the alarm will be triggered only when at least two sensors activate simultaneously.
Click button to learn how to use the Karnaugh Map to solve the problem in minutes!
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