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Truth Table

Truth Table. NOT AND NAND OR NOR XOR XNOR. Generate a Truth Table. NAND Based Logic Gates. Multiple Inputs Logic Gates. NOR Based Logic Gates. Sum of Products. A “sum of products” implementation outputs a 1 when one of the intermediates products is true. Home Alarm Logic.

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Truth Table

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  1. Truth Table • NOT • AND • NAND • OR • NOR • XOR • XNOR

  2. Generate a Truth Table

  3. NAND Based Logic Gates

  4. Multiple Inputs Logic Gates

  5. NOR Based Logic Gates

  6. Sum of Products • A “sum of products” implementation outputs a 1 when one of the intermediates products is true

  7. Home Alarm Logic

  8. Home Alarm Truth Table

  9. Sum of Products Equation • Parts • 12 inverters • 3 2-input AND gates for each 4-input AND gate. Therefore, 24 2-input AND gates. • 7 2-input OR gates.

  10. NAND Based Logic Gates

  11. Delay Calculations • Parts • 12 inverters (1 TTL delay) • 3 2-input AND gates for each 4-input AND gate. Therefore, 24 2-input AND gates. • Each AND gate: 2 TTL delay • For each 4-input ANDN gate: 4 TTL delay • 7 2-input OR gates. • 2 TTL delay for each OR gate • 7 2-input OR gates (6 TTL delay) • Total delay: 6 TTL delay+4 TTL delay+1 TTL delay=11 TTL delay

  12. Karnaugh Map for 2-Variables

  13. Karnaugh Map for 3-Variables

  14. Karnaugh Map for 4-Variables

  15. Looping • Groups of Two • Groups of Four • Group of Eight

  16. Looping Groups of Two

  17. Looping Groups of Four

  18. Solution for Problem 4

  19. Two Equally Solutions

  20. Boolean Algebra

  21. AND Identities (1)

  22. AND Identities (1) • +

  23. OR Identities (1)

  24. OR Identities (2) • ) (

  25. DeMorgan’s NOR Theorm • Invert each input • Swap an AND with an OR, and an OR with an AND.

  26. DeMorgan’s NAND Theorm • Invert each input • Swap an AND with an OR, and an OR with an AND.

  27. Home Alarm Example

  28. Sum of Product Expression

  29. Circuit Simplification Example

  30. Factoring—the first & third terms above haveACin common, which can be factored out: Since B + B = 1, then… z = A(C + B) Solution

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