L4+Boolean+Representation

L4+Boolean+Representation - Lecture 4 Expression of Logic...

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Ve270 Introduction to Logic Design 1 Lecture 4 Expression of Logic Functions
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Ve270 Introduction to Logic Design 2 Minterm and Maxterm A binary variable may assume two values: 0 or 1, represented by the primed form and unprimed forms respectively Minterm is a product of n literals in which each variable appears exactly once in either true or complemented form, but not both – Minterm is represented by m i Maxterm is a sum of n literals in which each variable appears exactly once in either true or complemented form, but not both – Maxterm is represented by M i
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Ve270 Introduction to Logic Design 3 Minterm and Maxterm m 7 m 6 m 5 m 4 m 3 m 2 m 1 m 0 Designation xyz xyz’ xy’z xy’z’ x’yz x’yz’ x’y’z x’y’z’ Term Minterms M 7 x’+y’+z’ 1 1 1 M 6 x’+y’+z 0 1 1 M 5 x’+y+z’ 1 0 1 M 4 x’+y+z 0 0 1 M 3 x+y’+z’ 1 1 0 M 2 x+y’+z 0 1 0 M 1 x+y+z’ 1 0 0 M 0 x+y+z 0 0 0 Designation Term z y x Maxterms Subscription i is the decimal equivalent of the corresponding binary combination
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Ve270 Introduction to Logic Design 4 Minterm in Truth Table 0 1 1 1 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 F result z con3 y con2 x con1 Result would happen if con1 is false AND con2 is false AND con3 is true , x’y’z Result would happen if con1 is false AND con2 is true AND con3 is true , x’yz Result would happen if con1 is true AND
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L4+Boolean+Representation - Lecture 4 Expression of Logic...

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