Boolean Algebra Applications1 BOOLEAN ALGEBRA APPLICATIONS RELIABILITY OF CIRCUITS
Boolean Algebra Applications2
3
4
5
6
7 Boolean Sum can be converted into arithmetic sum when we obtain a non-overlapping expression
Boolean Algebra Applications8
9
10
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
Boolean Algebra Applications21
Boolean Algebra Applications22
Boolean Algebra Applications23
Boolean Algebra Applications24
Boolean Algebra Applications25
Boolean Algebra Applications26
Boolean Algebra Applications27 K- Map Method
Boolean Algebra Applications28
Boolean Algebra Applications29
Boolean Algebra Applications30 Example:
Boolean Algebra Applications31
Boolean Algebra Applications32
Boolean Algebra Applications33
Boolean Algebra Applications34
Boolean Algebra Applications35
Boolean Algebra Applications36
Boolean Algebra Applications37
Boolean Algebra Applications38
Boolean Algebra Applications39
Boolean Algebra Applications40
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
Boolean Algebra Applications46
Boolean Algebra Applications47
Boolean Algebra Applications48
Boolean Algebra Applications49
Boolean Algebra Applications50
Boolean Algebra Applications51
Boolean Algebra Applications52
Boolean Algebra Applications53
Boolean Algebra Applications54
Boolean Algebra Applications55
Boolean Algebra Applications56
Boolean Algebra Applications57
Boolean Algebra Applications58
Boolean Algebra Applications59
Boolean Algebra Applications60
Boolean Algebra Applications61 Questions ?