ECE 3110: Introduction to Digital SystemsPrevious…Combination-circuit analysisSlide 4Signal expressionsNew circuit, same functionSlide 7“Add out” logic function (T8’)Another example: Symbol substitutionDifferent circuit, same functionNext… (Chapter 4.3.3-4.4)ECE 3110: Introduction to Digital SystemsCombinational-Circuit Analysis2Previous…Representations of Logic FunctionsTruth tableCanonical sum [e.g. X’.Y’+X.Y]Minterm list: on-setCanonical product [e.g. (X’+Y).(X+Y’) ]Maxterm list: off-set] )3,0( [,YXe.g.] )2,1( ..[,YXge3Combination-circuit analysisObtaining a formal description of its logic function. Why?Determine the behavior for various input combinationsManipulate an algebraic description to suggest different circuit structures.Transform a description into a standard form.Use the description in the analysis of a larger system.45Signal expressionsMultiply out (T8):F = ((X + Y) Z) + (X Y Z) = (X Z) + (Y Z) + (X Y Z)6New circuit, same functionFasterCosts moreTwo-level AND-OR7Signal expressionsAdd out (T8)?8“Add out” logic function (T8’)Two-level OR-AND?9Another example: Symbol substitution10Different circuit, same function11Next… (Chapter 4.3.3-4.4)Combinational circuit synthesisCombinational circuit minimizationKarnaugh
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