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-CA Lecture 5c: Digital Logic
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- Properties of Boolean Algebra
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-
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- Read Appendix A of textbook: p450 – p456
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-
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- (Not examined, except DeMorgan
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- theorem)
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-
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- 1
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- Properties of Boolean Algebra
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-
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- 2
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- Properties of Boolean Algebra
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- Cont.
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-
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-• The postulates are basic axioms of Boolean
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- algebra and therefore need no proofs.
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-
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-• The theorems can be proven from the
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- postulates.
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-
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-• Each relationship has both an AND form and
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- an OR form as a result of the principle of
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- duality.
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-
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-• The dual form is obtained by replacing AND
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- with OR and OR with AND, 1’s with 0’s, and
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- 0’s with 1’s.
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-
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- 3
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- Properties of Boolean Algebra
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-
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- Cont.
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-
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-• The commutative property states that the
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- order that two variables appear in an AND or
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- OR function is not significant.
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-
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-• The distributive property shows how a
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- variable is distributed over an expression.
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-
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-• The identity property states that a variable
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- that is ANDed with 1 or is ORed with 0
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- produces the original variable.
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-
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-• The complement property states that a
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- variable that is ANDed with its complement is
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- logically false, and a variable that is ORed
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- with its complement is logical true.
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-
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- 4
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- Properties of Boolean Algebra
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-
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- Cont.
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-
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-• The zero and one theorems state that a
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- variable that is ANDed with 0 produces a 0,
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- and a variable that is ORed with 1 produces a
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- 1.
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-
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-• The idempotence theorem states that a
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- variable that is ANDed or ORed with itself
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- produces the original variable.
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-
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-• The associative theorem states that the order
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- of ANDing or ORing is logically of no
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- consequence.
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-
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-• The involution theorem states that the
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- complement of a complement leaves the
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- original variable (or expression) unchanged. 5
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yeungalan