K-Map.pptx

K-Map

1. Prof. Neeraj Bhargava Mrs. Pooja Dixit Department of Computer Science, School of Engineering & System Sciences MDS University Ajmer, Rajasthan K-MAP

2. Minterm and Maxterm for three variables Minterm Maxterm XYZ Term Designation Term Designation 000 X’Y’Z’ M0 X+Y+Z M0 001 X’Y’Z M1 X+Y+Z’ M1 010 X’YZ’ M2 X+Y’+Z M2 011 X’YZ M3 X+Y’+Z’ M3 100 XY’Z’ M4 X’+Y+Z M4 101 XY’Z M5 X’+Y+Z’ M5 110 XYZ’ M6 X’+Y’+Z M6 111 XYZ M7 X’+Y’+Z’ M7

3. Minterm and Maxterm for three variables Q1. find the sum of product and product of sum: f= Σ (1,3,7) (S.O.P) (X’ Y’ Z) + (X’ Y Z) + (X Y Z) f= λ (1,3,7) (P.O.S) (X + Y + Z’) (X + Y’ + Z’) (X’ + Y’ + Z’)

4. K-Map K-Map method is a graphical technique for simplify boolean function. It is a 2-D representation of a Truth-Table. Karnaugh maps  reduce  logic functions more quickly and easily compared to Boolean algebra. By reduce we mean simplify, reducing the number of gates and inputs. A K-Map is a diagram consisting of squares and each square of the map represents minterm and maxterm .

5. 2-Variable K-Map It has 4 minterms map consist of 4 square. One for each minterm . 0 and 1 marked for each row and each column designate the values of variable x and y repectively 2 n = 2 2 = 4 cells .

6. Rules for K-Map Simplification Note: (Here generally we are taking sum of product expression rules) Groups may not contain Zero( means when we use Boolean expression with sum of product form then we use 1 otherwise we use 0) We can group 1,2,4,8 (2 n cells) Each group should be as large as possible. Cells containing 1 must be grouped. Groups may overlap. Opposite grouping and corner grouping is allowed. There should be as few group as possible.

7. 2-Variable K-Map Simplify the given 2-variable Boolean equation by using K-map. F = X Y’ + X’ Y + X’Y’ We put 1 at the output terms given in equation. In this K-map, we can create 2 groups by following the rules for grouping, one is by combining (X’, Y) and (X’, Y’) terms and the other is by combining (X, Y’) and (X’, Y’) terms. Here the lower right cell is used in both groups. After grouping the variables, the next step is determining the minimized expression. By reducing each group, we obtain a conjunction of the minimized expression such as by taking out the common terms from two groups, i.e. X’ and Y’. So the reduced equation will be X’ +Y’.

8. 2 Variable K-Map Ex1: AB+AB’+A’B So, the minimize expresion is: F=A+B Ex2 : F = ∑ (m , m 1 , m 2 ) = A̅B̅ +A̅B +AB̅ Q1: y= a’b+ab+ab ’ Q2: x’y+xy ’