# lec3 - CS 140 Lecture 3 Combinational Logic Professor CK...

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1 CS 140 Lecture 3 Combinational Logic Professor CK Cheng CSE Dept. UC San Diego

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2 1.Specification 1.Implementation 1.K-maps Part I Combinational Logic.
3 Literals x i or x i Product Term x 2 x 1 ’x 0 Sum Term x 2 + x 1 ’ + x 0 Minterm of n variables: A product of n literals in which every variable appears exactly once. Maxterm of n variables: A sum of n literals in which every variable appears exactly once. Definitions

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4 Implementation Specification Schematic Diagram Net list, Switching expression Obj min cost Search in solution space (max performance) Cost: wires, gates Literals, product terms, sum terms We want to minimize # of terms, # of literals
5 Implementation (Optimization) ID A B f(A,B) minterm 0 0 0 0 1 0 1 1 A’B 2 1 0 1 AB’ 3 1 1 1 AB An example of 2-variable function f(A,B)

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6 Function can be represented by sum of minterms: f(A,B) = A’B+AB’+AB This is not optimal however! We want to minimize the number of literals and terms. We factor out common terms – A’B+AB’+AB= A’B+AB’+ AB+AB =(A’+ A )B+A(B’+ B )=B+A Hence, we have f(A,B) = A+B
7 K-Map: Truth Table in 2 Dimensions A = 0 A = 1 B = 0 B = 1 0 2 1 3 0 1 1 1 A’B AB’ AB f(A,B) = A + B

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8 ID A B f(A,B) minterm 0 0 0 0 1 0 1 1 A’B 2 1 0 0 3 1 1 1 AB Another Example f(A,B)=A’B+AB=(A’+A)B=B
9 On the K-map: A = 0 A= 1 B= 0 B = 1 0 2 1 3 0 0 1 1 A’B AB f(A,B)=B

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lec3 - CS 140 Lecture 3 Combinational Logic Professor CK...

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