The simplified Boolean function contains all essential prime implicants and only the required prime implicants. Note down all the prime implicants and essential prime implicants. The prime implicant is said to be essential prime implicant, if atleast single ‘1’ is not covered with any other groupings but only that grouping covers. Highest power is equal to the number of variables considered in K-map and least power is zero.Įach grouping will give either a literal or one product term. Start from highest power of two and upto least power of two. If the Boolean function is given as sum of products form, then place the ones in all possible cells of K-map for which the given product terms are valid.Ĭheck for the possibilities of grouping maximum number of adjacent ones. If the Boolean function is given as sum of min terms form, then place the ones at respective min term cells in the K-map. Select the respective K-map based on the number of variables present in the Boolean function. Similarly, if we consider the combination of inputs for which the Boolean function is ‘0’, then we will get the Boolean function, which is in standard product of sums form after simplifying the K-map.įollow these rules for simplifying K-maps in order to get standard sum of products form. If we consider the combination of inputs for which the Boolean function is ‘1’, then we will get the Boolean function, which is in standard sum of products form after simplifying the K-map. Minimization of Boolean Functions using K-Maps Similarly, you can use exclusively the Max terms notation. In the above all K-maps, we used exclusively the min terms notation. If v=0, then 5 variable K-map becomes 4 variable K-map. i.e., grouping of min terms from m 0 to m 15 and m 16 to m 31. There are two possibilities of grouping 16 adjacent min terms. There is only one possibility of grouping 32 adjacent min terms. The following figure shows 5 variable K-Map. The number of cells in 5 variable K-map is thirty-two, since the number of variables is 5. If w=0, then 4 variable K-map becomes 3 variable K-map. The possible combinations of grouping 2 adjacent min terms are. There is only one possibility of grouping 4 adjacent min terms. The following figure shows 2 variable K-Map. The number of cells in 2 variable K-map is four, since the number of variables is two. Now, let us discuss about the K-Maps for 2 to 5 variables one by one. K-Map method is most suitable for minimizing Boolean functions of 2 variables to 5 variables. The adjacent cells are differed only in single bit position.
It is a graphical method, which consists of 2 n cells for ‘n’ variables. This method is known as Karnaugh map method or K-map method. To overcome this difficulty, Karnaugh introduced a method for simplification of Boolean functions in an easy way. It is a time consuming process and we have to re-write the simplified expressions after each step. In previous chapters, we have simplified the Boolean functions using Boolean postulates and theorems.
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