L3+Boolean+Algebra - Lecture 3 Boolean Algebra Ve270...

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Ve270 Introduction to Logic Design 1 Lecture 3 Boolean Algebra
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Ve270 Introduction to Logic Design 2 Boolean Algebra “Traditional” algebra – Variable represent real numbers – Operators operate on variables, return real numbers Boolean Algebra – Developed mid-1800’s by George Boole to formalize human thought – Variables represent 0 or 1 only – Operators return 0 or 1 only – Basic operators •AND : a AND b returns 1 only when both a=1 and b=1 •OR : a OR b returns 1 if either (or both) a=1 or b=1 •NOT
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Ve270 Introduction to Logic Design 3 Boolean Algebra Terminology Example equation: F(a,b,c) = a’bc + abc’ + ab + c Variable – Represents a value (0 or 1) – Three variables: a, b, and c Literal – Appearance of a variable, in true or complemented form – Nine literals: a’, b, c, a, b, c’, a, b, and c Product term – Product of literals – Four product terms: a’bc, abc’, ab, c Sum-of-products – Equation written as OR of product terms only – Above equation is in sum-of-products form. “F = (a+b)c + d” is not.
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L3+Boolean+Algebra - Lecture 3 Boolean Algebra Ve270...

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