Boolean Algebra Applications1 BOOLEAN ALGEBRA APPLICATIONS RELIABILITY OF CIRCUITS.

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Presentation transcript:

Boolean Algebra Applications1 BOOLEAN ALGEBRA APPLICATIONS RELIABILITY OF CIRCUITS

Boolean Algebra Applications2

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

Boolean Algebra Applications8

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Boolean Algebra Applications11 Non-overlapping expression using K-map

Boolean Algebra Applications12

Boolean Algebra Applications13 F & M METHOD L. Fratta & V. Montanari Discuss boolean algebra approach for determining terminal reliability

Boolean Algebra Applications14 Algorithm Determine all paths Write down the corresponding boolean expression Determine non-overlapping simplification Transform into mathematical expression Substitute reliability values

Boolean Algebra Applications15 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 Applications16 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 Applications17 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 Applications18 Example:

Boolean Algebra Applications19

Boolean Algebra Applications20 2. No stop 3. A= X1

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Boolean Algebra Applications27 K- Map Method

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Boolean Algebra Applications29

Boolean Algebra Applications30 Example:

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Boolean Algebra Applications41 X1X2

Boolean Algebra Applications42 X3X4

Boolean Algebra Applications43 X1X4X5

Boolean Algebra Applications44 X2X3X5

Boolean Algebra Applications45 Non-overlapping exp. using K-Map

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Boolean Algebra Applications61 Questions ?