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218L6F08a - ESE218 Lecture 6 Standard forms Two-level...

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9/18/08 ESE218 Fall 2008 Lecture 6 1 ESE218 Lecture 6. Standard forms. Two-level implementations Outline Standard forms SOP and POS, form conversion Canonical standard forms minterms, sum of minterms Maxterms, products of maxterms form conversion Implementations of algebraic expressions AND-OR vs NAND-NAND OR-AND vs NOR-NOR Open-drain, three-state and wired logic AOI and OAI Summary
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9/18/08 ESE218 Fall 2008 Lecture 6 2 Canonical standard forms SOP: F = ABD + C’D = ABD(C+C’)+(A+A’)(B+B’)C’D = = ABCD+ABC’D+ABC’D+A’BC’D+AB’C’D+A’B’C’D 1 POS: F = (A+C’)(B+C’)D = (A+BB’+C’+DD’)(AA’+B+C’+DD’)(AA’+BB’+CC’+D) = = (A+B+C’+DD’)(A+B’+C’+DD’)(...)(...) = = (A+B+C’+D) (A+B+C’+D’) (A+B+C’+D) (A+B’+C’+D’)(…)(…) 0 Canonical SOP is a sum of input combinations when function = 1 Canonical POS is a product of input combinations when function = 0 Simplification of an algebraic expression (combination of different terms) begins with presenting the expression in a canonical form as a sum of smallest pieces, i.e. cases when function =1 for the SOP form (or when function = 0 for the POS form)
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9/18/08 ESE218 Fall 2008 Lecture 6 3 minterms and Maxterms 7 6 5 4 3 2 1 0 # M 7
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