THE KARNAUGH MAP

What is Karnaugh Map?

    Karnaugh Map - is a method to simplify Boolean algebra expressions. The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability, also permitting the rapid identification and elimination of potential race conditions.

OVERVIEW OF KARNAUGH MAP

    In a Karnaugh map the boolean variables are transferred (generally from a truth table) and ordered according to the principles of Gray code in which only one variable changes in between adjacent squares. Once the table is generated and the output possibilities are transcribed, the data is arranged into the largest possible groups containing 2ⁿ cells (n=0,1,2,3...)^[1] and the minterm is generated through the axiom laws of boolean algebra.

 WHAT'S MORE ABOUT KARNAUGH MAP OR K-MAP?

    We will going to discussed about karnaugh maps (k-maps) and we have been discussing about truth tables where we have got our input and output variables. Since the truth table's binary and decimal numbers were being read respectively with the assigned input and output variables unlike the K-map. K-map's binary input and output variable together with the binary and decimal numbers were recognized in rows and in columns. The simple representation of truth table vs k-map are the following:

HOW TO IMPLEMENT K-MAPS?

   To implement k-maps, first we should consider it's minterms, what is minterms? minterm is a Boolean expression resulting in 1 for the output of a single cell, and 0s for all other cells in a Karnaugh map, or truth table. Supposedly, we have two statements or two inputs with one output. Since 2^n = 2^2 = 4, so we have four rows and the decimal numbers are counted up to 0, 1, 2, 3, and 4. Therefore, we have two rows and two columns for our k-map. Hence, putting the output 'F' in the k-map table, we can have our boolean expression 'A + B = F' to be able to get our logic or schematic diagram. Schematic diagram will be tackled on the proceeding blog.