Basic Electrical and Electronics Engineering: Unit IV: Digital Electronics
Karnaugh Map (K-MAP)
with Solved Example Problems
The K-map is a graphical technique for simplifying boolean expression.
KARNAUGH MAP (K-MAP) The K-map is a graphical technique for simplifying boolean expression. The K map is three dimensional representation of a truth table. This K-map technique is ideally suited for four or less variables. K-map can be a 2-variable K-map, 3-variable K-map; 4-variable K-map. The first row is for Ā and second for A. In the same way, first column is for B and second column for B. For any square, both row and column are observed. For first square of first row, Ā and Similarly, 0 and 1 logic are for Problem 4.44 Simplify with help of K-map. Solution : Problem 4.45 Simplify with help of K-map. Solution: Boolean simplification In group 1: In group 2: By summing both the results Y = A + B For three variables K-map, the ordering of the variables is done in gray code. Problem 4.46 Simplify the function Y = Solution: Problem 4.47 Simplify the expression Y = Solution : Hence the resulting expression is Problem 4.48 Simplify the expression Solution : Using K-map simplify the expression, Placing is in the respective squares, we observe that all the squares containing 1s are adjacent and so they can be grouped together to give A which is common to all squares. Therefore Y = A The representation of logical variables and product terms for four variables K- map is depicted in figure 4.12. Problem 4.49 Simplify the boolean expression. Solution : Problem 4.50 Simplify the boolean expression. Solution:Two variable K-map
are the variables and so this square indicates the product term or minterm 
Similarly, second square indicates ĀB. In map, 0 represents Ā and 1 represents A. and B respectively.
K-map for three variables
+ ABC using K-map method.
K-map for four variables
Basic Electrical and Electronics Engineering: Unit IV: Digital Electronics : Tag: : with Solved Example Problems - Karnaugh Map (K-MAP)
Basic Electrical and Electronics Engineering: Unit IV: Digital Electronics
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