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Switching & Finite Automata

by: Lizeth Hegmann

Switching & Finite Automata ECE 5520

Lizeth Hegmann
GPA 3.61

Frank Severance

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Frank Severance
Class Notes
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This 9 page Class Notes was uploaded by Lizeth Hegmann on Wednesday September 30, 2015. The Class Notes belongs to ECE 5520 at Western Michigan University taught by Frank Severance in Fall. Since its upload, it has received 33 views. For similar materials see /class/216785/ece-5520-western-michigan-university in Engineering Electrical & Compu at Western Michigan University.

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Date Created: 09/30/15
Chapter Six Functional Decomposition Shannan s39l henrem Func nn decomposition f xxx fxA0XIamp1 foch6010 sh401u g amu fwul Notes 1 If can always be accomphshed 2 11 Is easylo do You only xemove me vanable Seton 14an expansion fszO an 1 More general mctinnal decomposition px x2xm Notes 1 Rmchonsp and q amp is m 97 song1e4emo products 2 n someomes works 3 Implemenlahon ls nonrln nal Example uvwxyz 29u1522414355s9 uwx nv wx nu vw yx wx 1urv rw yz u x jlwxyz uvswyxeyol vov where pwxylwx l 1m W J39I Iv v Example using Shannon s theorem wawa w x z wx rw ynwyz 3 o23791o1114 Expand about 1 1 M00 w x M01 wx L 10wx nun wux Wmm y z w 2 y twx yz w x mm u 2 Expand alum1x y Lam w39nm mum x y bv zHvl x ylxy 0 uym nwz x yl lixly y x y x y xy x y Thus pxy x x 9 J v w1wz Decomposition Charts Column multiplicity The number of different column patterns of 039s and 139s is called the column multiplicity Row multiplicity The number of different row patterns of 039s and 139s is called the row multiplicity Basis signals The input variables of mctions p and q are called the basis of a decomposition off Decomposition Theorem If the decomposition chart for an expansion R of fx1 x2 x has column multiplicity of exactly two then f can be decomposed using R as the basis Notes 1 With 11 variables and k expansion variables there are different decomposition tables 2 Therefore the number tables is 2quot 3 By observing row multiplicities as well as column multiplicities the number of different tables is reduced to 2 n to l n ifneven 0 2 n2 n to quot ifnodd o n12 Example 11 4 fwxyz k0 wxyz 0123456789101112131415 k1 k2 xyz yz w01234567 0123 89101112131415 wx4567 891011 12131415 Wyz x0123 891011 456712131415 quotz 0145 wy 2367 891213 W 10111415 y0145 891213 236710111415 xy wxy 0246 z02468101214 wz1357 13579111315 8101214 9111315 Example fvwxyz E 34579151721222829 21 1013141823273031 Using both row and column multiplicity tests there are 1 0gtlt32 variables table 5 1gtlt4 variables table 10 2gtlt 10 variables table 1 Try expanding about v y z vyzwx 00 01 10 11 000 0 4 8 12 001 1 5 9 13 010 2 6 10 14 011 3 7 11 15 100 16 20 24 28 101 17 21 25 29 110 18 22 26 30 111 19 23 27 31 2 Try expanding about x z xzva 000 001 010 011 100 101 110 111 00 0 2 8 10 16 18 24 26 01 1 3 9 11 17 19 25 27 10 4 6 12 14 20 22 28 30 11 5 7 13 15 21 23 29 31 Amgn demure sandman nnn um am an 1nn 1n1 11n 111 1 2 1247 vwy f xz xz1 x zxl 454quot


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