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Class Note for ECE 380 at UA-Digital Logic(3)

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Alabama - Tuscaloosa taught by a professor in Fall. Since its upload, it has received 21 views.

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Date Created: 02/06/15
ECE380 Digital Logic Optimized Implementation of Logic Functions Multilevel Synthesis and Analysis Electrical amp Computer Engineering Dr D J Jackson Lecture 151 Multilevel NAND amp NOR circuits o Twolevel circuits consisting of AND and OR gates can easily be converted to networks that can be realized only NAND and NOR gates A twolevel ANDOR SOP circuit can be realized directly as a twolevel NANDNAND circuit A twolevel ORAND POS circuit can be realized directly as a twolevel NORNOR circuit 0 The same approach can be used for multilevel networks Electrical amp Computer Engineering Dr D J Jackson Lecture 152 ANDOR to NANDNAND example Electrical amp Computer Engineering Dr D J Jackson Lecture 15quot ORAND to NORNOR example Electrical amp Computer Engineering Dr D J Jackson Lecture 154 Multilevel example Multilevel example NAN D dwfux bk 9 Circuit with AND and OR gates gtlt bx wxnx Mgtlt mxm x Inversions needed to convert to NANDs Note the inversion bubbles added to the output of every AND gate and to the input of every OR gate Also the inversion bubbles are always placed in pairs nrnJJclsnn Lemuelss z lmnul x cannula Enunml39 Elainel x Carmina Englrumu m n J Indian Lain 155 Multilevel example NAN D Multilevel example NOR X7 Conversion to a NANDgate circuit Elainel x cannula Enuneallu m n J has LemuelSJ X1 X2 X3 r X4 X5 X6 X7 Inversions needed to convert to NORs Note the inversion bubbles added to the output of every OR gate and to the input of every AND gate Also the inversion bubbles are always placed in pairs Elainel x Carmina Englrumu m n J Indian Lain 151 Multilevel example NOR X1 quot2 3 f X4 X5 X6 X7 Conversion to a NORgate circuit Electrical a computer Engineering Dr oJ Jackson Lecture lse Multilevel conversion process o The basic topology wiring of a circuit does not change substantially when converting from AND and OR gates to either NAND or NOR gates o It may be necessary to insert additional gates to serve as NOT gates that implement inversions not absorbed as a part of other gates in the circuit 0 The resulting circuit may not be minimum ie such as a minimum 2Ievel NANDNAND or NORNOR network Electrical amp computer Engineering Dr D J Jackson Lecture 1510 Multilevel conversion example What is the NAND only equivalent of the following circuit 3 Electrical a computer Engineering oroJ Jackson Lecture 1511 Analysis of multilevel circuits In the previous examples we synthesized multilevel circuits How can we easily determine a function that a given multilevel circuit implements For twolevel circuits we simply wrote out the SOP or POS form equation from the circuit This is easy to visualize for twolevel circuits This is more difficult for multilevel circuits because it is difficult to write an expression for the circuit by inspection We can write an expression for a function by analyzing it at intermediate points in the circuit Write expressions for each of these subfunctions Combine the subfunctions together into a single function Electrical amp computer Engineering Dr D J Jackson Lecture 1512 Multilevel circuit analysis Label the output of every gate as a subfunction Electrical it computer Engineering Dr DJ Jackson Lecture 1513 Multilevel circuit analysis 0 Combine and simplify if possible these functions P1X1X2 P2X1X3 P3P1P2X4 X1X2X1X3X4X1X3X4X2X1X3X4 X1X3X4 P4X1P3 X1X1X3X4 X1X3X4 X1IX3IX4l P5X3X4 f P3 P4 P5 X1X3X4 X1X3X4 X3X4 1 Electrical it computer Engineering Dr D J Jackson Lecture 1514

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