1、Boolean Algebra Review ISE 741 North Carolina State University Boolean Algebra •Developed by English mathemaAcian, George Boole, for study of symbolic logic: –Principles and concepts of Boolean Algebra can be useful in system safety engineering, parAcu
2、larly in fault tree analysis and accident invesAgaAon. •Two‐state system (there are only two values) “yes” or “no”; “on” or “off”; “true” or “false”; “up” or “down”; “go” or “no go”; “right” or wrong”; “1” or “0” •Boolean algebra (algebra of events)
3、 defines event operaAons that are represented by various symbols. Symbology differs as follows: OperaAon Probability MathemaAcs Engineering Union of A and B A OR B A∪B A + B IntersecAon of A and B A AND B A∩B A●B or AB Complement of A NOT A A’ or A A
4、’ or A 2 Boolean Logic Applicability Safety Analysis •Boolean logic has pracAcal applicaAon in relaAon to fault tree analysis –A fault tree can be thought of as a pictorial representaAon of Boolean relaAonships between variables –A fault tree can be tr
5、anslated into an equivalent set of Boolean equaAons •Understanding the rules of Boolean algebra contributes toward the construcAon and/or simplificaAon of fault trees –Once a fault tree has been drawn, it can be evaluated using Boolean logic to idenAfy
6、its quanAtaAve characterisAcs •These characterisAcs cannot be directly observed from the fault tree, but they can be obtained from the equivalent Boolean equaAons 3 Symbolic Boolean Logic In fault tree analysis the most useful form of Boolean logic are
7、 the “AND” and “OR”condiAons also known as "gates“ YYOR (+) AND (●) Probability of event “Y” OR operaAon: will be true if at least one of its inputs are true will return false only if all terms are false AND operaAon: will be true only if all of its in
8、puts are true 4 Boolean Algebra •OR operaAonscan be represented by addiAon or the "+" sign –Thus "A + B" would read "A" OR "B" •The addiAon property of OR carries essenAally the same properAes as normal addiAon For example: Truth Table
