03_LCD_Slide_Handout_1(16) - Boolean Algebra Defined...

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*Property of STI K0028 BOOLEAN ALGEBRA Simplification of Boolean Expression Through Postulates and Theorems Boolean Algebra Defined Sum of Products and Product of Sums Form 1 _________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Boolean Algebra Defined What is Boolean algebra? It was named after George Boole (1815 – 1864) and was adapted in 1938 by Claude Shannon 2 __________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Boolean Algebra Defined What is Boolean algebra? It is a form of algebra that consists of: set of elements: E = {true, false} or E = {on, off}, {1, 0}, {high, low} set of operators: O = {NOT {'}, AND { }, OR {+}} 3 _________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Boolean Algebra Defined Truth table for the Boolean NOT operator A A’ 0 1 1 0 4 __________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________
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*Property of STI K0028 Boolean Algebra Defined Truth table for the Boolean AND operator A B A B 0 0 0 0 1 0 1 0 0 1 1 1 5 _________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Boolean Algebra Defined Truth table for the Boolean OR operator A B A + B 0 0 0 0 1 1 1 0 1 1 1 1 6 __________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Boolean Algebra Defined The 16 Possible Boolean Functions of Two Variables 7 _________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Boolean Algebra Defined The 16 Possible Boolean Functions of Two Variables 8 __________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________
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*Property of STI K0028 Simplification of Boolean Expression Through Postulates and Theorems Precedence of Operators Precedence level Operator 1 Brackets/Parenthesis ( ) 2 Boolean complement NOT 3 Boolean product AND 4 Boolean sum OR 9 _________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Simplification of Boolean Expression Through Postulates and Theorems Practice Exercises Evaluate the following expression: F = D (BC’A + (AB’ + C)’ + C); when A = 0, B = 0, C = 1, D = 1 10 _________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Simplification of Boolean Expression Through Postulates and Theorems Practice Exercises Evaluate the following expression: F = A’BC (A+D)’; when A = 0, B = 1, C = 1, D = 1 F = [D + ((A + B)C)’]E; when A = 0, B = 0, C = 1, D = 1, E = 1 11 ________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ *Property of STI K0028 Simplification of Boolean Expression Through Postulates and Theorems Postulates (or axioms) These are given facts that are accepted as true without a proof 12 _________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________ ___________________________
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*Property of STI K0028 Simplification of Boolean Expression Through Postulates and Theorems Postulates (or axioms) It is also known as the Huntington’s Postulate , which refers to a set of rules defined on how a set of numbers can
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