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?
𝑃 𝐷 𝑊1 𝑊2
𝑃 𝐷𝑊1 𝑊2
What about
these terms?

5. Exercise
Use the following properties to simplify the home alarm logic:
X ∙(Y+Z)=X ∙ Y+X ∙ Z
𝑋+ 𝑋 =1

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
𝑓1= 𝑥 𝑦 𝑧+𝑥 𝑦 𝑧 +𝑥𝑦𝑧

11. f1 Form a maxterm for each term that produces a 0
AND all of those terms
𝑓1=(𝑥+𝑦+𝑧)(𝑥+ 𝑦 +𝑧) (𝑥+ 𝑦 + 𝑧 )( 𝑥 +𝑦+ 𝑧 )( 𝑥 + 𝑦 +𝑧)
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 F2 A B C 1

14. F1 A B C 1