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BOOLEAN ALGEBRA APPLICATIONSRELIABILITY OF CIRCUITS
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Boolean Sum can be converted into arithmetic sumwhen we obtain a
non-overlapping expression
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Boolean Algebra Applications*
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Non-overlapping expression using K-map
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Boolean Algebra Applications
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F & M METHODL. Fratta & V. Montanari
Discuss Boolean algebra approach for determining terminal
reliability
Boolean Algebra Applications
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AlgorithmDetermine all pathsWrite down the corresponding Boolean
expressionDetermine non-overlapping simplificationTransform into
mathematical expressionSubstitute reliability values
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AlgorithmStep 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
non-complemented variables corresponding to the arcs in the
path
Boolean Algebra Applications
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AlgorithmLet P = 0
Step 2:If f has no terms, stopStep 3:Select any term A of fStep
4:Let A be the arithmetic monomial which is equivalent to A
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Boolean Algebra Applications*Algorithm
Let P = P + A _Step 5: Let A f f and reduce f to a sum of
products. Go to step 2.
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Example:
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K- Map Method
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Example:
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X1X2
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X3X4
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X1X4X5
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X2X3X5
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Non-overlapping exp. using K-Map
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Boolean Algebra Applications*Questions ?
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