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K-Map.pptx

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Pooja Dixit

The document discusses Karnaugh maps, which are a graphical technique for simplifying boolean functions. A K-map is a diagram with squares that each represent minterms or maxterms. Variables are represented along rows and columns. Groups of 1s can be combined according to grouping rules to simplify boolean expressions. The example shows a 2-variable K-map used to minimize the boolean expression XY' + X'Y + X'Y' to X' + Y'. K-maps allow boolean functions to be reduced more easily than boolean algebra.

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K-MAP
Minterm Maxterm XYZ Term Designation Term Designation 000 XYZ M0 X+Y+Z M0 001 XYZ M1 X+Y+Z M1 010 XYZ M2 X+Y+Z M2 011 XYZ M3 X+Y+Z M3 100 XYZ M4 X+Y+Z M4 101 XYZ M5 X+Y+Z M5 110 XYZ M6 X+Y+Z M6 111 XYZ M7 X+Y+Z M7
Q1. find the sum of product and product of sum: f= 裡(1,3,7) (S.O.P) (XY Z) + (XY Z) + (XY Z) f=了 (1,3,7) (P.O.S) (X +Y + Z) (X +Y + Z) (X +Y + Z)
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.
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 2n = 22= 4 cells.
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 (2n 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.
Simplify the given 2-variable Boolean equation by using K-map. F = XY + XY + XY 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 andY. So the reduced equation will be X +Y.
Ex1: AB+AB+AB So, the minimize expresion is: F=A+B Ex2 : F = (m0, m1, m2) = AB +AB +AB Q1: y=ab+ab+ab Q2: xy+xy

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K-Map.pptx

  • 2. Minterm Maxterm XYZ Term Designation Term Designation 000 XYZ M0 X+Y+Z M0 001 XYZ M1 X+Y+Z M1 010 XYZ M2 X+Y+Z M2 011 XYZ M3 X+Y+Z M3 100 XYZ M4 X+Y+Z M4 101 XYZ M5 X+Y+Z M5 110 XYZ M6 X+Y+Z M6 111 XYZ M7 X+Y+Z M7
  • 3. Q1. find the sum of product and product of sum: f= 裡(1,3,7) (S.O.P) (XY Z) + (XY Z) + (XY Z) f=了 (1,3,7) (P.O.S) (X +Y + Z) (X +Y + Z) (X +Y + Z)
  • 4. 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. 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 2n = 22= 4 cells.
  • 6. 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 (2n 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. Simplify the given 2-variable Boolean equation by using K-map. F = XY + XY + XY 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 andY. So the reduced equation will be X +Y.
  • 8. Ex1: AB+AB+AB So, the minimize expresion is: F=A+B Ex2 : F = (m0, m1, m2) = AB +AB +AB Q1: y=ab+ab+ab Q2: xy+xy