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1、u Switching algebrau Representations of the logic functionu Logic circuit design Chapter 4 Combinational logic design principlesMinimization of the logic circuit by Karnaugh mapKarnaugh map and its propertyRelation between karaugh map and logic equationsSteps for minimization Karnaugh map2D Figure f
2、or truth tableProperties of Karnaugh mapThe coordinates are ordered in Gray codes;Each cell differs from its neighbors in only one variable!Standard logic equation and their Karnaugh map Minterm listMaxterm listLogic equations and their Karnaugh map Sum of product Product of sum Same logic with diff
3、erent forms Properties of neighbor cellsCan be minimized by karnaugh map Get a minimal product-sum equationMinimal sumStep 1:Make rectangular sets of 1s u Cover all the 1s in the Kanaugh maps;u The cell-numbers in any sets must be 2i;u The number of sets must be minimal!u Each set must be maximal!(A
4、ny 1s can be reused in the process!)Step 1:Make rectangular sets of 1s Minimal sumStep 2:write minimal sum from sets of 1su Write each set as a product;for 2i-set,the product have(n-i)variables!u Sum all these products.Minimal sumMinimal sumMinimal sumMinimal sumMinimal sumMinimal sumImply:a rectang
5、ular set of 1s;Prime implicant:a maxim imply;Complete sum:sum of all the prime implicant;Distinguished 1-cell:only in one prime implicant;Essential prime implicant:with distinguished 1-cell in it.Some conceptGet a minimal sum-product equationMinimal productStep 1 get minimal sum for inverse functionStep 2 use DeMorgens theorem to get minimal product of the function Minimal product