LOGIC3-1_r2 - Microwave & Communication Lab....

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Unformatted text preview: Microwave & Communication Lab. Chapter 3-1 Boolean Algebra (Continued) Microwave & Communication Lab. De Morgans laws (X 1 +X 2 +X 3 ++X n )=X 1 X 2 X n (X 1 X 2 X n )=X 1 +X 2 +X 3 ++X n (proof by ? ? ? ) The complement of the product is the sum of the complements. The complement of the sum is the product of the complements . Inversion Microwave & Communication Lab. EX Find the complement of (A+B)C Sol [(A+B)C]=(A+B)+(C) =(A)B+C =AB+C Microwave & Communication Lab. One-step rule for applying De Morgans laws To form the complement of a Boolean expression, replace each variable with its complement, replace 0 with 1, 1 with 0, + with ., and with +. i.e. [f(x 1 ,x 2 , ,x n ,0,1,+, )]=f(x 1 ,x 2 , ,x n ,1,0, ,+) Microwave & Communication Lab. *In applying this rule, we must carefully preserve the proper hierarchy of operations by adding (or deleting) parentheses as required . *AND is performed before OR, unless parentheses indicate the order. Microwave & Communication Lab. EX [(AB+C)D+E]=[(A+B)C+D]E EX [(A+B)C]=AB+C Microwave & Communication Lab. Given a Boolean expression, the dual of the expression is formed by replacing AND with OR, OR with AND, 0 with 1, and 1with 0....
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This note was uploaded on 10/23/2011 for the course EE 101 taught by Professor Wang during the Spring '11 term at Illinois State.

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LOGIC3-1_r2 - Microwave & Communication Lab....

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