Applied Electronics Unit 2 Karnaugh Maps.pptx

K Maps

1. Physics Practical III Dr. B. Prakash, Assistant Professor, Arul Anandar College, Karumathur Applied Electronics (20PPYE22) -Karnaugh Map Dr. B. Prakash Assistant Professor P.G and Research Department of Physics Arul Anandar College (Autonomous) Karumathur – 625 514.

2. Karnaugh Maps (K maps)

3. What are Karnaugh 1 maps? Karnaugh maps provide an alternative way of simplifying logic circuits . Instead of using Boolean algebra simplification techniques, you can transfer logic values from a Boolean statement or a truth table into a Karnaugh map . The arrangement of 0's and 1's within the map helps you to visualise the logic relationships between the variables and leads directly to a simplified Boolean statement . 1 Named for the American electrical engineer Maurice Karnaugh.

4. Karnaugh maps Karnaugh maps, or K - maps, are often used to simplify logic problems with 2, 3 or 4 variables . For the case of 2 variables, we form a map consisting of 2 2 =4 cells as shown in Figure A B 1 1 Cell = 2 n ,where n is a number of variables 00 10 01 11 A B 1 1 A B 1 1 Maxterm Minterm 2 1 3

5. Karnaugh maps 3 variables Karnaugh map AB C 00 01 11 10 1 2 6 4 5 3 1 7 Cell = 2 3 =8

6. Karnaugh maps 4 variables Karnaugh map AB CD 00 01 11 10 00 01 11 10 5 3 1 7 6 2 4 9 15 13 11 10 14 12 8

7. Karnaugh maps The Karnaugh map is completed by entering a '1‘(or ‘0’) in each of the appropriate cells . Within the map, adjacent cells containing 1's (or 0’s) are grouped together in twos, fours, or eights .

8. Example A B Y 1 1 1 1 1 1 1 2-variable Karnaugh maps are trivial but can be used to introduce the methods you need to learn . The map for a 2-input OR gate looks like this : A B 1 1 1 1 1 B A A+B

9. Example A B C Y 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 AB C 00 01 11 10 1 1 1 1 1 1

10. Rules to obtain the most simplified expression Simplification of logic expression using Boolean algebra is awkward because: it lacks specific rules to predict the most suitable next step in the simplification process it is difficult to determine whether the simplest form has been achieved. A Karnaugh map is a graphical method used to obtained the most simplified form of an expression in a standard form (Sum-of-Products or Product-of-Sums). The simplest form of an expression is the one that has the minimum number of terms with the least number of literals (variables) in each term. By simplifying an expression to the one that uses the minimum number of terms, we ensure that the function will be implemented with the minimum number of gates. By simplifying an expression to the one that uses the least number of literals for each terms, we ensure that the function will be implemented with gates that have the minimum number of inputs.

11. Three-Variable K-Maps

12. Four-Variable K-Maps

13. Design of combinational digital circuits Steps to design a combinational digital circuit: From the problem statement derive the truth table From the truth table derive the unsimplified logic expression Simplify the logic expression From the simplified expression draw the logic circuit Example: Design a 3-input (A,B,C) digital circuit that will give at its output (X) a logic 1 only if the binary number formed at the input has more ones than zeros.

14. Design of combinational digital circuits (Cont.) Example: Design a 4-input (A,B,C,D) digital circuit that will give at its output (X) a logic 1 only if the binary number formed at the input is between 2 and 9 (including).

15. Solving K-Map : An Experimental Approach

16. Thank You