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Chapter 4

Chapter 4. Logic Gates and Boolean Algebra. Introduction. Logic gates are the actual physical implementations of the logical operators . These gates form the basic building blocks for all digital logic circuits . Logic gates process signals which represent true or false.

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Chapter 4

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  1. Chapter 4 Logic Gates and Boolean Algebra

  2. Introduction • Logic gates are the actual physical implementations of the logical operators. • These gates form the basic building blocks for all digital logic circuits. • Logic gates process signals which represent true or false.

  3. Introduction • Gates are identified by their function: NOT, AND, NAND, OR, NOR, EX-OR and EX-NOR. Switch S1 AND Switch S2 must be closed to light the lamp Switch S1 OR Switch S2 (or both of them) must be closed to light the lamp

  4. Truth Table • A truth table is a means for describing how a logic circuit's output depends on the logic levels present at the circuit's inputs.

  5. Logic Gates and Circuit Diagrams • OR Gate

  6. Logic Gates and Circuit Diagrams • AND Gate

  7. Logic Gates and Circuit Diagrams • NOT Gate

  8. Logic Gates and Circuit Diagrams • NOR Gate

  9. Logic Gates and Circuit Diagrams • NAND Gate

  10. Logic Gates and Circuit Diagrams • EX-OR gate The 'Exclusive-OR' gate is a circuit which will give a high output if either but not both, of its two inputs are high. • EX-NOR gate is The inversion of EX-OR Gate

  11. Describing Logic Circuits Algebraically

  12. Describing Logic Circuits Algebraically

  13. Evaluating Logic Circuit Outputs

  14. Evaluating Logic Circuit Outputs

  15. Determining Output Level from a Diagram

  16. Implementing Circuits From Boolean Expression

  17. Boolean Algebra • Simplification of logical circuits. • One tool to reduce logical expressions is the mathematics of logical expressions. • The rules of Boolean Algebra are simple and straight-forward, and can be applied to any logical expression.

  18. Boolean Algebra

  19. Boolean Algebra

  20. Boolean Algebra (A’B)’(A+B) Solution: (A + B’) (A + B) AA + B’A + AB + B’B A + B’A + AB A + AB A AB(A + B’C +C) Solution: ABA + ABB’C + ABC AB + 0 + ABC AB + ABC AB

  21. Boolean Algebra

  22. Universality of NAND & NOR Gates

  23. Universality of NAND & NOR Gates

  24. Alternate Logic Gate Representations

  25. Forms and Definitions of Boolean Expressions

  26. Product of Sums Representation

  27. Disjunctive Normal Form

  28. Disjunctive Normal Form

  29. Disjunctive Normal Form

  30. Disjunctive Normal Form Using truth tables, convert this expression into a sum of minterms

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