Sum of Products Section 2.7.

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Presentation transcript:

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

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

W1=0V, P=W2=5V

P=W1=5V, W2=0 V

Minterm/maxterm

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

Example 𝑓1= 𝑥 𝑦 𝑧+𝑥 𝑦 𝑧 +𝑥𝑦𝑧

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

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

Exercise F2 A B C 1

F1 A B C 1