Karnaugh map or kmap
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Karnaugh map or kmap

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Its a presentation about Karnaugh Map or Kmap...If u use it and get help from it...pls thank me in my email......

Its a presentation about Karnaugh Map or Kmap...If u use it and get help from it...pls thank me in my email...
Email Address: iamwasim@yahoo.com

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  • 1. Digital System Design Presentation : 1 Ihr Logo
  • 2. Introduction  Name: MD. Wasim Akram  ID: UG 02 22 09 016  Department: CSEPage 2 Your Logo
  • 3. Topic Karnaugh MapPage 3 Your Logo
  • 4. What is Karnaugh Map•The Karnaugh map (K-map for short), Maurice Karnaughs 1953 refinementof Edward Veitchs 1952 Veitch diagram, is a method to simplify Booleanalgebra expressions.•The Karnaugh map reduces the need for extensive calculations by takingadvantage of humans pattern-recognition capability, also permitting the rapididentification and elimination of potential race conditions.•Definition: A Karnaugh map provides a pictorial method of grouping togetherexpressions with common factors and therefore eliminating unwanted variables.The Karnaugh map can also be described as a special arrangement of a truthtable.•A visual way to simplify logic expressions•It gives the most simplified form of the expressionPage 4 Your Logo
  • 5. 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.Page 5 Your Logo
  • 6. Continued 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 inputsPage 6 Your Logo
  • 7. Simplification Process in Bullet Points:  No zeros allowed.  No diagonals.  Only power of 2 number of cells in each group.  Groups should be as large as possible.  Every one must be in at least one group.  Overlapping allowed.  Wrap around allowed.  Fewest number of groups possible.Page 7 Your Logo
  • 8. Three-Variable K-Maps f = ∑ (0,4) = B C f = ∑ (4,5) = A B f = ∑ (0,1,4,5) = B f = ∑ (0,1,2,3) = A BC BC BC BC A 00 01 11 10 A 00 01 11 10 A 00 01 11 10 A 00 01 11 10 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 f = ∑ (0,4) = A C f = ∑ (4,6) = A C f = ∑ (0,2) = A C f = ∑ (0,2,4,6) = C BC BC BC BC A 00 01 11 10 A 00 01 11 10 A 00 01 11 10 A 00 01 11 10 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1Page 8 Your Logo
  • 9. Four-Variable K-Maps CD CD CD CD AB 00 01 11 10 AB 00 01 11 10 AB 00 01 11 10 AB 00 01 11 10 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 1 0 0 01 0 0 0 0 01 1 0 0 1 11 0 0 0 0 11 0 1 0 0 11 0 1 1 0 11 0 0 0 0 10 1 0 0 0 10 0 0 0 0 10 0 0 0 0 10 0 0 0 0 f = ∑(0,8) = B • C • D f = ∑(5,13) = B • C • D f = ∑(13,15) = A • B • D f = ∑(4,6) = A • B • D CD CD CD CD AB 00 01 11 10 AB 00 01 11 10 AB 00 01 11 10 AB 00 01 11 10 00 0 0 1 1 00 0 0 0 0 00 0 0 1 1 00 1 0 0 1 01 0 0 1 1 01 1 0 0 1 01 0 0 0 0 01 0 0 0 0 11 0 0 0 0 11 1 0 0 1 11 0 0 0 0 11 0 0 0 0 10 0 0 0 0 10 0 0 0 0 10 0 0 1 1 10 1 0 0 1 f = ∑(2,3,6,7) = A • C f = ∑(4,6,12,14) = B • D f = ∑(2,3,10,11) = B • C f = ∑(0,2,8,10) = B • DPage 9 Your Logo
  • 10. 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 zerosPage 10 Your Logo
  • 11. Continued Inputs Output A B C X X = ∑ (3, 5, 6, 7) 0 0 0 0 0 1 0 0 1 0 X BC 2 0 1 0 0 A 00 01 11 10 3 0 1 1 1 0 0 0 1 0 4 1 0 0 0 1 0 1 1 1 5 1 0 1 1 6 1 1 0 1 7 1 1 1 1 X = AC + AB + BC A B CPage 11 Your Logo
  • 12. Dont cares Functions  Karnaugh maps also allow easy minimizations of functions whose truth tables include "dont care" conditions (that is, sets of inputs for which the designer doesnt care what the output is) because "dont care" conditions can be included in a circled group in an effort to make it larger. They are usually indicated on the map with a dash or X.Page 12 Your Logo
  • 13. What are the Advantages of Karnaugh Maps?  The primary advantage of a Karnaugh map is the data representation’s simplicity. The map’s grid structure simplifies the arrangement of similar variables that can group and disperse like terms to identify and resolve potential issues in the design.  Changes in neighboring variables are easily displayed, permitting the engineer to view cause and effect relationships.  Easy and Convenient to implement.  As a result, digital circuit and information theory industries still use Karnaugh maps today.Page 13 Your Logo
  • 14. Referrence  Wikipedia.com  Digital System Design Book  Digital Design by Morris Mano  Verilog Digital System Design by Zainalabedin NavabiPage 14 Your Logo
  • 15. Conclusion  To conclude this presentation, I would like to say Thank you Madam and the Class….Page 15 Your Logo
  • 16. Questions? ????Page 16 Your Logo