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Fundamentals of Boolean Algebra: Tables, Gates, and Implementations

Dive into the postulates, theorems, and practical applications of Boolean algebra with tables, gates, and truth tables for different functions. Explore implementations of logic gates for various Boolean functions in digital systems.

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Fundamentals of Boolean Algebra: Tables, Gates, and Implementations

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  1. Table 2.1 Postulates and Theorems of Boolean Algebra

  2. Table 2.2 Truth Tables for F1 and F2

  3. FIGURE 2.1 Gate implementation of F1 = x + y’z

  4. FIGURE 2.2 Implementation of Boolean function F2 with gates

  5. Table 2.3 Minterms and Maxterms for Three Binary Variables

  6. Table 2.4 Functions of Three Variables

  7. Table 2.5 Truth Table for F = A + B’C

  8. Table 2.6 Truth Table for F = xy + x’z

  9. FIGURE 2.3 Two‐level implementation

  10. FIGURE 2.4 Three‐ and two‐level implementation

  11. Table 2.7 Truth Tables for the 16 Functions of Two Binary Variables

  12. Table 2.8 Boolean Expressions for the 16 Functions of Two Variables

  13. FIGURE 2.5 Digital logic gates

  14. FIGURE 2.6 Demonstrating the nonassociativity of the NOR operator:

  15. FIGURE 2.7 Multiple‐input and cascaded NOR and NAND gates

  16. FIGURE 2.8 Three‐input exclusive‐OR gate

  17. FIGURE 2.9 Signal assignment and logic polarity

  18. FIGURE 2.10 Demonstration of positive and negative logic

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