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A four variable K-map is used to simplify a complex Boolean expression in 4 variables. As we know, a four variable Boolean expression can have 2 4 = 16 possible combinations of variables. For example, in SOP (Sum of Products) Form,
- Steps to Solve Expression Using K-Map
- Sop Form
- Pos Form
Select the K-map according to the number of variables.Identify minterms or maxterms as given in the problem.For SOP put 1’s in blocks of K-map respective to the minterms (0’s elsewhere).For POS put 0’s in blocks of K-map respective to the max terms (1’s elsewhere).1. K-map of 3 variables
From redgroup we get product term— Fromgreengroup we get product term— Summing these product terms we get- Final expression (A’C+AB)
2. K-map for 4 variables
From redgroup we get product term— From greengroup we get product term— Summing these product terms we get- Final expression (QS+Q’S’).
1. K-map of 3 variables
From red group we find terms Taking complement of these two Now sumup them Frombrowngroup we find terms Taking complement of these two terms Now sum up them From yellow group we find terms Taking complement of these two Now sumup them We will take product of these three terms : Final expression –
2. K-map of 4 variables
From greengroup we find terms Taking their complement and summing them From redgroup we find terms Taking their complement and summing them From bluegroup we find terms Taking their complement and summing them From brown group we find terms Taking their complement and summing them Finally we express these as product – PITFALL–*Always remember POS ? (SOP)’ *The correct form is (POS of F)=(SOP of F’)’ Quiz on K-MAP
K-Map is used for minimization or simplification of a Boolean expression. 2-4 variable K-maps are easy to handle. However, the real challenge is 5 and 6 variable K-maps. Visualization of 5 & 6 variable K-map is a bit difficult. When the number of variables increases, the number of the square (cells) increases.
Larger 4-variable Karnaugh Maps. PDF Version. Knowing how to generate Gray code should allow us to build larger maps. Actually, all we need to do is look at the left to right sequence across the top of the 3-variable map, and copy it down the left side of the 4-variable map. See below.
Let us now proceed to understand how 4 variable K-map gets realized. Karnaugh map for 4 variables In case of realizing 4 variable K-map, the number of cells will be 2 4 i.e., 16.
Sep 24, 2021 · Thus, this is all about an overview of Karnaugh maps– definition, rules, use, 5 variable K-map, 4 variable or 4×4 K-map, and some solved examples. By using karnaugh maps, BCD (binary coded decimal) code can be converted into Gray code very easily and quickly.
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Grouping Minterms. The next crucial step in K Map simplification is to group the adjacent minterms (1s). Groups must be in powers of 2 (1, 2, 4, 8, etc.). Adjacency can be top, bottom, left, or right, and even wrap around edges: One 1: Isolated cell. Two 1s: Horizontal or vertical pair. Four 1s: Form a rectangle encompassing four adjacent cells.
