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Chapter 5

Chapter 5. Boolean Algebra and Reduction Techniques. 1. 5-5 DeMorgan’s Theorem. Used to simplify circuits containing NAND and NOR gates A B = A + B A + B = A B. DeMorgan’s Theorem. Break the bar over the variables and change the sign between them

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Chapter 5

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  1. Chapter 5 Boolean Algebra and Reduction Techniques 1

  2. 5-5 DeMorgan’s Theorem • Used to simplify circuits containing NAND and NOR gates • A B = A + B • A + B = A B

  3. DeMorgan’s Theorem • Break the bar over the variables and change the sign between them • Inversion bubbles - used to show inversion. • Use parentheses to maintain proper groupings • Results in Sum-of-Products (SOP) form

  4. Figure 5.38 De Morgan’s theorem applied to NAND gate produces two identical truth tables.

  5. Figure 5.39 (a) De Morgan’s theorem applied to NOR gate produces two identical truth tables;

  6. More examples

  7. 1. Change the logic gate (AND to OR or OR to AND) 2.Add bubbles to the inputs and outputs where there were none and remove original bubbles Bubble Pushing

  8. 5-7 The Universal Capability of NAND and NOR Gates • An inverter can be formed from a NAND simply by connecting both NAND inputs as shown in Figure 5-68.

  9. More examples Figure 5-69 Forming an AND with two NANDs

  10. Figure 5-70, 5-71 (Equivalent logic circuit using only NANDs

  11. Fig 5-72 External connections to form the circuit of Fig 5-71.

  12. Figure 5-73 Forming an OR from there NANDs. Figure 5-74 Forming a NOR with four NANDs

  13. Discussion Point • The technique used to form all gates from NANDs can also be used with NOR gates. • Here is an inverter: • Form an inverter from a NOR gate. 29

  14. 5-8 AND-OR-INVERT Gates for Implementing Sum-of-Products Expressions

  15. AND-OR-INVERT Gates for Implementing Sum-of-Products Expressions 30

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