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BOOLEAN ALGEBRA

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BOOLEAN ALGEBRA

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  1. BOOLEAN ALGEBRA Boolean Algebra

  2. BOOLEAN ALGEBRA -REVIEW Boolean Algebra was proposed by George Boole in 1853. Basically AND,OR NOT can be expressed as Venn Diagrams Boolean Algebra

  3. Boolean Algebra

  4. Boolean Algebra

  5. Boolean Algebra

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  15. Min Terms and Max Terms Min Terms are those which occupy minimum area on Venn Diagram Max Terms are those which occupy maximum area on Venn diagram. Boolean Algebra

  16. Boolean Algebra

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  18. Boolean Algebra

  19. LOGIC GATES Nand and Norgates are calledUniversal gates as any Boolean function can be realized with the help of Nand and Nor gates only Boolean Algebra

  20. For example, NOT, OR, AND gates can be realized by only Nand gates. Boolean Algebra

  21. Boolean Algebra

  22. Boolean Algebra

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  25. SIMPLIFICATION OF BOOLEAN FUNCTIONS • Algebraic Method • Tabular Method • K-Map Method • Schienman Method Boolean Algebra

  26. ALGEBRAIC METHOD • Simplify using algebraic theorems • Advantage: • First Method based on Boolean Algebra theorems • Disadvantage: • No Suitable algorithm to apply (Trial type of method) Boolean Algebra

  27. TABULAR METHOD • Also called Quine McClusky Method • Advantage: • It may work for any no. of variables • Disadvantage: • Simplification from table is quite involved Boolean Algebra

  28. K-MAP METHOD • Karnaugh Map. Also called Vietch • Karnaugh Method. • Advantage: • Simplest and Widely accepted • Disadvantage: • Applicable for only upto Six variables Boolean Algebra

  29. SCHIENMAN METHOD • Columnwise writing of minterms as • decimal numbers and their simplification • Advantage: • Very suitable for computerization. Applicable for any • number of variables. Parallel Processing • Disadvantage: • May not result in most simplified answer for some • problems Boolean Algebra

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  38. Steps for simplification: • Try to find single one’s • 2 one’s • 4 one’s • 8 one’s Always see is a higher combination exists. If a higher combination exists, wait. Be sure that you have managed the lower combination first. Boolean Algebra

  39. Boolean Algebra

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