boolean algebra applications1 boolean algebra applications reliability of circuits

61
Boolean Algebra Applicati ons 1 BOOLEAN ALGEBRA APPLICATIONS RELIABILITY OF CIRCUITS

Post on 19-Dec-2015

244 views

Category:

Documents


6 download

TRANSCRIPT

Boolean Algebra Applications 1

BOOLEAN ALGEBRA APPLICATIONS

RELIABILITY OF CIRCUITS

Boolean Algebra Applications 2

Boolean Algebra Applications 3

Boolean Algebra Applications 4

Boolean Algebra Applications 5

Boolean Algebra Applications 6

Boolean Algebra Applications 7

Boolean Sum can be converted into arithmetic sumwhen we obtain a non-overlapping expression

Boolean Algebra Applications 8

Boolean Algebra Applications 9

Boolean Algebra Applications 10

Boolean Algebra Applications 11

Non-overlapping expression using K-map

Boolean Algebra Applications 12

Boolean Algebra Applications 13

F & M METHOD

L. Fratta & V. Montanari

Discuss boolean algebra approach for determining terminal reliability

Boolean Algebra Applications 14

Algorithm

• Determine all paths

• Write down the corresponding boolean expression

• Determine non-overlapping simplification

• Transform into mathematical expression

• Substitute reliability values

Boolean Algebra Applications 15

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 16

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 17

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 18

Example:

Boolean Algebra Applications 19

Boolean Algebra Applications 20

• 2. No stop

• 3. A= X1

Boolean Algebra Applications 21

Boolean Algebra Applications 22

Boolean Algebra Applications 23

Boolean Algebra Applications 24

Boolean Algebra Applications 25

Boolean Algebra Applications 26

Boolean Algebra Applications 27

K- Map Method

Boolean Algebra Applications 28

Boolean Algebra Applications 29

Boolean Algebra Applications 30

Example:

Boolean Algebra Applications 31

Boolean Algebra Applications 32

Boolean Algebra Applications 33

Boolean Algebra Applications 34

Boolean Algebra Applications 35

Boolean Algebra Applications 36

Boolean Algebra Applications 37

Boolean Algebra Applications 38

Boolean Algebra Applications 39

Boolean Algebra Applications 40

Boolean Algebra Applications 41

X1X2

Boolean Algebra Applications 42

X3X4

Boolean Algebra Applications 43

X1X4X5

Boolean Algebra Applications 44

X2X3X5

Boolean Algebra Applications 45

Non-overlapping exp. using K-Map

Boolean Algebra Applications 46

Boolean Algebra Applications 47

Boolean Algebra Applications 48

Boolean Algebra Applications 49

Boolean Algebra Applications 50

Boolean Algebra Applications 51

Boolean Algebra Applications 52

Boolean Algebra Applications 53

Boolean Algebra Applications 54

Boolean Algebra Applications 55

Boolean Algebra Applications 56

Boolean Algebra Applications 57

Boolean Algebra Applications 58

Boolean Algebra Applications 59

Boolean Algebra Applications 60

Boolean Algebra Applications 61

Questions ?