BOOLEAN ALGEBRA APPLICATIONS RELIABILITY OF CIRCUITS Boolean Algebra

BOOLEAN ALGEBRA APPLICATIONS RELIABILITY OF CIRCUITS Boolean Algebra Applications 1

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Boolean Sum can be converted into arithmetic sum when we obtain a non-overlapping expression Boolean Algebra Applications 7

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Non-overlapping expression using K-map Boolean Algebra Applications 11

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F & M METHOD L. Fratta & V. Montanari Discuss boolean algebra approach for determining terminal reliability Boolean Algebra Applications 13

Algorithm • Determine all paths • Write down the corresponding boolean expression • Determine non-overlapping simplification • Transform into mathematical expression • Substitute reliability values Boolean Algebra Applications 14

Algorithm Step 1: Let S be the set of all simple paths between the terminal nodes. Construct a Boolean sum of products f, where each product corresponds to a path S and whose factors are exactly the noncomplemented variables corresponding to the arcs in the path Boolean Algebra Applications 15

Algorithm Let P = 0 Step 2: If f has no terms, stop Step 3: Select any term A of f Step 4: Let A’ be the arithmetic monomial which is equivalent to A Boolean Algebra Applications 16

Algorithm Let P = P + A’ Step 5: Let A’. f --> f and reduce f to a sum of products. Go to step 2. Boolean Algebra Applications 17

Example: Boolean Algebra Applications 18

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• 2. No stop • 3. A= X 1 Boolean Algebra Applications 20

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K- Map Method Boolean Algebra Applications 27

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Example: Boolean Algebra Applications 30

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X 1 X 2 Boolean Algebra Applications 41

X 3 X 4 Boolean Algebra Applications 42

X 1 X 4 X 5 Boolean Algebra Applications 43

X 2 X 3 X 5 Boolean Algebra Applications 44

Non-overlapping exp. using K-Map Boolean Algebra Applications 45

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Questions ? Boolean Algebra Applications 61