Karnaugh Map, very commonly know as K-Map is a graphical device used to simplify a logic equation or to convert a truth table to its corresponding logic circuit in a simple orderly process. K-map is like a truth table, which shows the relationship between logic inputs and desired outputs.
Karnaugh Map, is a diagram made up of squares and is used to simplify and reduce the boolean expressions. A decimal numerical value is assigned to each cell and the labeling of the cells is done in such a manner that only one variable changes at a time. A ‘0’ denotes a complemented variable and “1” an un-complemented variable. K-Map can be created for 3-variable, 4-variable, 5-variable and so on. A k-variable K-Map has 2k cells. Below diagram is of a 3-variable K-Map:
At a time only one variable is changing from complemented to un-complemented & vice-versa as we move from one cell to next. Carefully note numbering of these cells. We will understand more about each of the 3-variable, 4-variable, 5-variable and 6-variable K-Map in next posts.
Boolean expressions can be simplified by using Logic Fundamentals as well. Sometime back, we shared couple of examples of reducing boolean expressions by using logic fundamentals – you may download it from here.
In this tutorial we will learn reducing and simplifying boolean expressions by using K-Map. For ease of understanding, we have divided the tutorial into 7 parts. Last 4 parts explains when to use each of these K-Maps and how to simplify them for a given function F.
- Understanding Minterms & Maxterms
- Rules of Simplifying K-Map
- 3-Variable K-Map
- 4-Variable K-Map
- 5-Variable K-Map
- 6-Variable K-Map
We hope that you find this series of articles on Karnaugh Map helpful and easy to understand. Please leave your footprints in the comments section below for any queries, feedback or suggestions…!!