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Sum of Products

Sum of Products. Section 2.7. Home Alarm Example. (Truth Table). (Boolean Algebra). Truth Table. Definition: Alarm Response (AR) Sound Alarm→AR =1 Else: AR=0. (Truth Table). Determine a Boolean Function from a Truth Table. When is AR=1 ?. What about these terms ?. Exercise.

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Sum of Products

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  1. Sum of Products Section 2.7

  2. Home Alarm Example (Truth Table) (Boolean Algebra)

  3. Truth Table Definition: Alarm Response (AR) Sound Alarm→AR=1 Else: AR=0 (Truth Table)

  4. Determine a Boolean Function from a Truth Table When is AR=1? What about these terms?

  5. Exercise • Use the following properties to simplify the home alarm logic: • X ∙(Y+Z)=X ∙ Y+X ∙ Z • +

  6. W1=0V, P=W2=5V

  7. P=W1=5V, W2=0 V

  8. Minterm/maxterm

  9. Minterms Procedure: Form a minterm for each combination of the variables that produces a 1 OR all the minterms.

  10. Example

  11. f1 Form a maxterm for each term that produces a 0 AND all of those terms Interpretation: Each maxterm can zero out f1

  12. Standard Forms • The minterm representation leads to Sum of Products implementation • The maxterm representation leads to Products of Sums implementation

  13. Exercise

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