ࡱ>  /bjbjVV .D<<'%00sssss84$'t"   ZB,nb'd'd'd'd'd'd'$W)+'s'ss  'Zs s b'b'r,&T& `{u&N''0'&,,&&n,s 'D''&',0 9: Course: Computer Architecture Topic: Karnaugh Maps Lecture 5 So far we can see that applying Boolean algebra can be awkward in order to simplify expressions. Apart from being laborious (and requiring the remembering all the laws) the method can lead to solutions which, though they appear minimal, are not. The Karnaugh map provides a simple and straight-forward method of minimizing boolean expressions. With the Karnaugh map Boolean expressions having up to four and even six variables can be simplified. So what is a Karnaugh map? A Karnaugh map provides a pictorial method of grouping together expressions with common factors and therefore eliminating unwanted variables. The Karnaugh map can also be described as a special arrangement of a  HYPERLINK "http://www.ee.surrey.ac.uk/Projects/Labview/common/glossary.html" \l "tt" truth table. The diagram below illustrates the correspondence between the Karnaugh map and the truth table for the general case of a two variable problem.  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/karintro1.gif" \* MERGEFORMATINET  The values inside the squares are copied from the output column of the truth table, therefore there is one square in the map for every row in the truth table. Around the edge of the Karnaugh map are the values of the two input variable. A is along the top and B is down the left hand side. The diagram below explains this:  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/karintro2.gif" \* MERGEFORMATINET  The values around the edge of the map can be thought of as coordinates. So as an example, the square on the top right hand corner of the map in the above diagram has coordinates A=1 and B=0. This square corresponds to the row in the truth table where A=1 and B=0 and F=1. Note that the value in the F column represents a particular function to which the Karnaugh map corresponds. Karnaugh maps, or K-maps, are often used to simplify logic problems with 2, 3 or 4 variables. 2-variable Karnaugh maps are trivial but can be used to introduce the methods you need to learn. The map for a 2-input OR gate looks like this:  INCLUDEPICTURE "http://homepages.westminster.org.uk/electronics/Sixth%20Form/SF%20images/k_01.gif" \* MERGEFORMATINET  Examples Example 1: Consider the following map. The function plotted is: Z = f(A,B) = A INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET  + AB  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/karexample1.gif" \* MERGEFORMATINET  Note that values of the input variables form the rows and columns. That is the logic values of the variables A and B (with one denoting true form and zero denoting false form) form the head of the rows and columns respectively. Bear in mind that the above map is a one dimensional type which can be used to simplify an expression in two variables. There is a two-dimensional map that can be used for up to four variables, and a three-dimensional map for up to six variables. Using algebraic simplification, Z = A INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET  + AB Z = A( INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET  + B) Z = A Variable B becomes redundant due to Boolean Theorem T9a. Referring to the map above, the two adjacent 1's are grouped together. Through inspection it can be seen that variable B has its true and false form within the group. This eliminates variable B leaving only variable A which only has its true form. The minimised answer therefore is Z = A. Example 2: Consider the expression Z = f(A,B) =  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/a.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET + A  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET +  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/a.gif" \* MERGEFORMATINET B plotted on the Karnaugh map:  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/karexample2.gif" \* MERGEFORMATINET  Pairs of 1's are grouped as shown above, and the simplified answer is obtained by using the following steps: Note that two groups can be formed for the example given above, bearing in mind that the largest rectangular clusters that can be made consist of two 1s. Notice that a 1 can belong to more than one group. The first group labelled I, consists of two 1s which correspond to A = 0, B = 0 and A = 1, B = 0. Put in another way, all squares in this example that correspond to the area of the map where B = 0 contains 1s, independent of the value of A. So when B = 0 the output is 1. The expression of the output will contain the term  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET  For group labelled II corresponds to the area of the map where A = 0. The group can therefore be defined as  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/a.gif" \* MERGEFORMATINET . This implies that when A = 0 the output is 1. The output is therefore 1 whenever B = 0 and A = 0 Hence the simplified answer is Z =  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/a.gif" \* MERGEFORMATINET +  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET  Verify this algebraically in your notebooks.  Problems Minimise the following problems using the Karnaugh maps method. Z = f(A,B,C) =  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/a.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/c.gif" \* MERGEFORMATINET +  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/a.gif" \* MERGEFORMATINET B + AB INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/c.gif" \* MERGEFORMATINET  + AC Z = f(A,B,C) =  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/a.gif" \* MERGEFORMATINET B + B INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/c.gif" \* MERGEFORMATINET  + BC + A INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/b.gif" \* MERGEFORMATINET  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/c.gif" \* MERGEFORMATINET  Karnaugh Maps - Rules of Simplification  The Karnaugh map uses the following rules for the simplification of expressions by grouping together adjacent cells containing ones. Adjacent cells Consider the following map. The function plotted is  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/common/graphics/adjac1.gif" \* MERGEFORMATINET   INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/common/graphics/adjac2.gif" \* MERGEFORMATINET  Using algebraic simplification,  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/common/graphics/adjac3.gif" \* MERGEFORMATINET by using T9a of the Boolean Laws (A +  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/common/graphics/adjac4.gif" \* MERGEFORMATINET = 1). Referring to the map we can encircle the adjacent cells and infer that A and  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/common/graphics/adjac4.gif" \* MERGEFORMATINET are not required. If two occupied cells of a Karnaugh are adjacent, horizontally or vertically (but not diagonally) then one variable is redundant. This has resulted by labelling the map as shown, i.e. adjacent cells satisfy the condition A +  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/common/graphics/adjac4.gif" \* MERGEFORMATINET = 1. Groups may not include any cell containing a zero  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/g1.gif" \* MERGEFORMATINET  Groups may be horizontal or vertical, but not diagonal.  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/g2.gif" \* MERGEFORMATINET  Groups must contain 1, 2, 4, 8, or in general 2n cells. That is if n = 1, a group will contain two 1's since 21 = 2. If n = 2, a group will contain four 1's since 22 = 4.  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/g3.gif" \* MERGEFORMATINET  Each group should be as large as possible.  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/g4.gif" \* MERGEFORMATINET  Each cell containing a one must be in at least one group.  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/g5.gif" \* MERGEFORMATINET  Groups may overlap.  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/g6.gif" \* MERGEFORMATINET  Groups may wrap around the table. The leftmost cell in a row may be grouped with the rightmost cell and the top cell in a column may be grouped with the bottom cell.  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/g7.gif" \* MERGEFORMATINET  There should be as few groups as possible, as long as this does not contradict any of the previous rules.  INCLUDEPICTURE "http://www.ee.surrey.ac.uk/Projects/Labview/minimisation/graphics/g8.gif" \* MERGEFORMATINET   Summary: No zeros allowed. No diagonals. Only power of 2 number of cells in each group. Groups should be as large as possible. Every one must be in at least one group. Overlapping allowed. Wrap around allowed. Fewest number of groups possible.     PAGE  PAGE 1 2=>?x  G H S T U \ _ `a׽ןןןןדxrןן hT=0JjhXZUjhXZU hXZhXZhXZhn_jhT=UjhT=Uh` hT=0J>*B*ph h` hT=jh` hT=UhT=6B*]phh` hT=h8hn_OJQJ^Jh8h8OJQJ^Jh8OJQJ^J*4>?6 W T92S^gdT= & Fdd[$\$gdT=gdT=$a$gdXZgdXZgdXZgdT=gdT= &d P gdT=gd8PQRSXYDEFGyPQRT6789;<DEFGY`hT=6B*]phjz<hT=Uj6hT=Ujl1hT=Uj+hT=Uj^&hT=U hT=0J hn_hT=j hT=UjRhT=UjhT=UhT=jhT=Uj+hT=U:NU:P!3#4#\#^####'\(^(gdgdgdgd^gdT=^gdT=^gdT=6789    z{|~\ ] ^ _ a b F!G!H!I!_!`!!!!j;rhT=UjlhT=Uj*ghT=UjahT=Uj\hT=UjVhT=UjUhT=UhT=6B*]phjqPhT=UjJhT=UjaEhT=Uj?hT=UjhT=UhT=9!!!!C"D"E"F"O"P""""".#/#0#1#3#4#\#]#######'$($$$$$$$%%%%)%*%%%%%%%,&-&.&/&&&&&ӹӱӱӱӱӱӱӱӱӱӱjhUjKhUjyhUjhUjhU hn_hh6B*]phj[hUhh` j҂hT=UjL}hT=UjwhT=UhT=jhT=U7&&&''S(T(U(V(^((((())))=)>)))))))* *V*W*^*_*******l+m+n+o+++++,,ƻưܨܨܨƝƒ܁!hT=h56B*\]phjh5U\j:h5U\h5H*\j h5U\jRh5U\jh5U\h5B*\ph h5\j§hUhjhUj2hU/^())*p+,,-........./(/R/h/~///// & Fdd[$\$gdgd & Fdd[$\$gd,,,3,4,,,,,M-N-----+.,..........///////////////////////⽵hn_0JmHnHu h80Jjh80JUh^1jh^1U h0JhjhUh8jh5U\jh5U\jwh5U\ h5\jh5U\jh5U\0///////////////h]hgd &`#$gdc,1h/ =!"#$% Dd X  S 4Akarintro1b M̼oWD|nM̼oWPNG  IHDRU]PLTEٟtRNS0JbKGDH cmPPJCmp0712OmNIDATX1O@ vʖߠ*6>@4cC110 U1lP9*$l=|-/^j"|">=VcWreaA[]ҝ:F۔`Yxk]g&Cʉ?݀`nYac~iҞ9!;Zխkz󀱖ٿ"ߎ%U{b0X7 +_XuKmu5VǺmlDuUlM9ޝUt)34.h%ĺUu)5^Dfe|_ѷz*d2;Oh=%ia;{TXA!dM} ZosS^[F}9*`cVXbqnev^~-IjcfA`YƎ=d87M/&zj0}{(&[?)8;DZsoMK[1'XDߌo볔dã]9*ln=pvMA2[o:4yTgqW G!\ߘ]WW'|Z j|Ul\x q[-Ӫbno59[+ =wWp)d;_eݧvJ:z\o*p NS_ ]FF+^CD+^W8.OٕR,~{&6b1w+|xdbqIc9EL37}{QxK:P^B̛x2mz;6rWyRw1NXw!ou tW/dhgIENDB`5 Ddhv  S RA *k_01OR gate Karnaugh mapbk & ȼ$4lG :|n? & ȼ$4lPNG  IHDREbAPLTEs@tRNSSbKGDH cmPPJCmp0712HsIDATx^b AA.!3*N< L&h" ERD@ؠIAaZ$E j3̥a^!bk6;e^ad##E0a\ĕq38͇EE{tnmlk3˶6 ߨI6ERD@ؠIAa=ZfOY7B_Cki 5 uA8Jg{:2AXT( ĜwQ,c$ń ^ RLQLzFRS,-$ڽ NKSvZ${Wx-Ee;x|χzoB2H:xJ={i g?^C,HqǡD 3H2R TU?\E}jDИbë=I=uNrIDBX!~QTohq_s N5`4>BͫbLԆ6p^iRW㻶IqOy~q9 Pt~Ok _b*0IW~R,iq.kZLx/N1vEFZih]@q|GAQ@R,5I{H1GQ^%#HGhOO_鄱NXGY _FFo8'وV+[{{ƀn=#?q{q $.קJ5 ȇuQ~(q.H1֝>AeiJ(yfΝNg"׫⫤H=MmtC*LiuiqXTv\ERD$ERD@ؠIAaZ$E j6ERD@ؠIAɓ_0P~"RnϣE`H/ 0t`\]#D..,R$E=ߍER+Q~بZt1 RD$ER -Fjc$|QR$G%ERDaW@"')"H= bsq\-Oˇ|X?LyM*la`ҺBDWcuFǮ4#borZϷ,҃jD1GRTȷT@I6ERD@ؠIA m%ͻ"B^W$sRHojZDȎI2íiZtRHqC" riEFbcE&4݄+s3)"H"bUG46H1H")" lP A-"!KIENDB`DdH  S $AbbFEX5 o|nFEX5PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`Dd b\  S 8Akarexample1bu2";)8lOÆ|nu2";)8lOÆPNG  IHDR~Ӌ PLTEKXtRNS0JbKGDH cmPPJCmp0712Om0IDATXM `h]̞Ifp xJKϨ&Ĕm4g pBpRCTpQiaTО*(uHY+LIeta5Et4HnK2Nbjj)3jiX15ut UV諂K;PAi"x řRl\q,o 8(>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`DdH   S $AbbFEX5 !|nFEX5PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`DdH   S $Aab( d-RJ&|n( d-RJPNG  IHDR } PLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs9IDATWc g ]C1@C $509I<*0jAWO]IENDB`Dd&8H   S $AbbFEX5 *,|nFEX5PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`Dd&8H   S $Ab bFEX5 1|nFEX5PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`DdH  S $Aa b( d-RJ67|n( d-RJPNG  IHDR } PLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs9IDATWc g ]C1@C $509I<*0jAWO]IENDB`aDd| | \  S 8Akarexample2 b{$1{}* ?<|n{$1{}* ?PNG  IHDRf PLTEKXtRNS0JbKGDH cmPPJCmp0712OmIDATh͎0`H$MnMtƽ!Zˤea|s/?E q{P  ]wJAB[IHtA$?{ZP mP a+9!`HsC2(/>(c 9C(J !*P!]Aє#T?ns(esO-'׈KξFlpbq Pt=}8&.FAsDufOO ֪ݘ@k EAQ%_'ʑ 13%"a!wO֪yn3 AYPޯ^)ڠHy.<s|EEw{IR*fus?Ҫn+y >ǯ Z*xN@):'t 7"odlqۅ>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`DdH  S $Aa b( d-RJE|n( d-RJPNG  IHDR } PLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs9IDATWc g ]C1@C $509I<*0jAWO]IENDB`DdH  S $Aab( d-RJ-K|n( d-RJPNG  IHDR } PLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs9IDATWc g ]C1@C $509I<*0jAWO]IENDB`DdH  S $AbbFEX5 P|nFEX5PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`Dd!<P  3 3"((DdH  S $Aab( d-RJV|n( d-RJPNG  IHDR } PLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs9IDATWc g ]C1@C $509I<*0jAWO]IENDB`Dd&8H  S $AbbFEX5 _\|nFEX5PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`DdH  S $AcbRɻ {4/a|nRɻ {4/PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs:IDATW0BDf9W! >>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs9IDATWc g ]C1@C $509I<*0jAWO]IENDB`Dd&8H  S $AcbRɻ {4/l|nRɻ {4/PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs:IDATW0BDf9W! >>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs9IDATWc g ]C1@C $509I<*0jAWO]IENDB`Dd&8H  S $AcbRɻ {4/x|nRɻ {4/PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs:IDATW0BDf9W! >>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDATWeN )2P 1#Ew$XK>}拾ͪVY7Z|IENDB`Dd&8H  S $AcbRɻ {4/|nRɻ {4/PNG  IHDR cuLPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs:IDATW0BDf9W! >>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs)IDATHKV -}^EI0ƕ^WݮQw+ܣV0z'D\ޱtIBo(Ibʤr^X+LG #%dݪ04#RT"}HH\NǨF#HCPcEi!@){)L=cht" x*PqA^cZ<0N7J++Vk>K8bHPp |/, 4(5x)2[-J@$2U5_3c4C;0Ũ|g0S* ?Mn 5ƢIENDB`DdR  S .A adjac2b,E.P|nE.PPNG  IHDRyqwPLTEjtRNS AbKGDH cmPPJCmp0712HsvIDAThCXۢ RKr΅m)!jַe $!'/N{ag3z2)5]zՃGfɢ@m*Ctj))Vr^eE ]04؞L4AvjI#S #0lP Ǚo5f}p8s^|l"\CE%HZzy^8lwD04XOjB V|C~@VsoBIN>/ȪZKH}7*IŤX=[ճw~U|KGv RcF[)P3 +_(Fvxy@_r >ԟd wl;2zh[_փ`[z(,60^iT"םhS>_SoVſUg)YU7#ہRv-1`8pYiكŨۦq ekty.?"pe+BIENDB`WDdYR  S .A adjac3b |8K-zEz|n |8K-zEzPNG  IHDRvKPLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712HsIDATHKU ;- !v=e}H0֎-_ziAֿ4ODXOο`$]G6Tk0Tr\0q\ĮqM+[4ISsj$QayY-X2z 3jԧHhKZ=-@H7XQdD~,,D?mCmaE]n,-tx_̠ +'3YƲsws\ֈYҏ6~|NIENDB`DdR   S .A adjac4b,쭑cP>V|n,쭑cP>VPNG  IHDR@t=PLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDAT(Sc `(MY L3 AA.Dȣ3QPm[ cIENDB`DdR ! S .A adjac4b,쭑cP>Vv|n,쭑cP>VPNG  IHDR@t=PLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDAT(Sc `(MY L3 AA.Dȣ3QPm[ cIENDB`Dd4?R " S .A adjac4 b,쭑cP>V|n,쭑cP>VPNG  IHDR@t=PLTE  !!!"""###$$$%%%&&&'''((()))***+++,,,---...///000111222333444555666777888999:::;;;<<<===>>>???@@@AAABBBCCCDDDEEEFFFGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPQQQRRRSSSTTTUUUVVVWWWXXXYYYZZZ[[[\\\]]]^^^___```aaabbbcccdddeeefffggghhhiiijjjkkklllmmmnnnooopppqqqrrrssstttuuuvvvwwwxxxyyyzzz{{{|||}}}~~~]}tRNSS%bKGDH cmPPJCmp0712Hs7IDAT(Sc `(MY L3 AA.Dȣ3QPm[ cIENDB` Dd4J # S &A g1!b GkJ |n GkJPNG  IHDR1PLTE @tRNS0JbKGDH cmPPJCmp0712HshIDATx^] r Lތi hI`Da>$qf2ā|p3 )`gaHCP<3 C 3ʑy' ;쯝@oED~~+&Tv:sm'*{Qվ}9v6ʄc3 /χʉ`)G: ="8bV Õ}3/P K\]q OIª̝ 2@^}<f/I4^E Nz*k:m@oC5FbL f˜Cfe f"J"hf$N 3tb7b 3pCdSxČ ( 8071b qn;AYT 1!܌(İ`\#Q8P gc¸]mGBF^3w}tg/ ؃GLiku:{%@OcySBP ]ӗT33}Y&Kf44r3 fdk ѩĸ~@Kf6 @4x=3w~e;g4(p3LTxzL[F2u!LV-7*>k.vJШ|b< 3:3@ׯ7gw3+ hj@ ^uvF> BCzrT}7;<3Jy&q+<6cH}CF-Gշ}hd ̌5ZOgQ3x#^Ovln=m'3 4?cX,(glcHŒ Q]ƨ<B3Nb84s5 h< @}BG"| j2\9Ȍٻ) 6__[5ˌ{L4:{RBfP[rǶH ׮u^hrK^SPЍgxM`-&nFM\?%ФY-odF<&נ3_ނeUp}Pi_RXf4Y"f^7cǭ-s.xfXM E\,8%33,M<3<3bf5Oaho9$ Z'w3&*81AY"gmᴁR|suyiW-'*(syx{8iߞ÷dK!Xhfq!xy"~PAC/ H%N,0nj ^\> mڙce#e?;-gU:NxzB1xd&pFГ.IЯ_MfF]>'dSQ5)0I:U Qex4,e/-R2VTvrvGBK׸H)dF>| 5U-8V2Rq+S>r3-S JhM^΍f֌y f)+7}YN -0e fL1#tL*}!|riu,i\!<GrEVa{} "5)haU70!(n! Ap3 )`gaHCP<3 C fR CfOIENDB`-Dd4J $ S &Ag2"bYxcjG,}~kQ|ncYxcjG,}~PNG  IHDR{15 PLTEKXtRNS0JbKGDH cmPPJCmp0712OmIDAThˎ8 @)"v4'RDYYp_9N[sU)u#'RoƛbxEXX 9^KH(CV0y d30`1ƚ0+x1tu1La@1!M,(E~&&͑:}2=V}E!ac%kTA&>e8ݛɰy Ucv@mH2}ɰvc7n&nQ6ޕ'RED0 b15$hœXi-J,cIlk(RZY%6F-O>Fs&}Uyvhvap~?] ;U$h{\UNfqqݓ;2fHHёIFVu_`7v$QtXM18۹s=fGbJ2+1:׌~t2KooAiM⌿w Ch 016y!? cY:AWK!#v̤`]L1[A3ڸur&1QȄٝڶcŪ˦'0DJkUseK> wh;,uuKrۼ1 P,"ݏp|nÐ`i;{dhѦ2FWC]3)DJd4R !!F QwYF;~ۏ~  BjTǰNkU`c]T@A/Bn^ĥS!PVJJ<6gCSQyD@@=L5m 0?6hpEҹ0>wZV|4S[eQxіqzBQw-_ˆg3r) 5Kv!*Fe(a̒VXG8gMnHh  ns"5{>(RXD?ĺvsQDQ7hvZ0y\R2'b--}.mWxA][}kxXõڕ+PWOkWlvv7[Xegπ~+P e= şQ.@qvŽcܺDyȜsFʼ,H-95eDPR˂}J{/B ,3P|5TVv(]b(քP *ݖA9P= % `Z@%XRb٬_bRP JA)(B~^XIENDB`Dd/1 J & S &Ag4$b#4>9)J 04|n4>9)J 0PNG  IHDR׌ PLTEKXtRNS0JbKGDH cmPPJCmp0712OmbIDATx͎(Ajz[êhiC bCl'5`̟ m'|$2Hf\Қ@C(͔djPLK֠f<|%-"2e.Yi4`6SI<2e.YȜ"2e.rJ%K!)s^>>MIZN4fNoc *|Ő}.FqLV 2Gc6e퇗"KXGgXGSzj"!F՚d|&&[k+K[ l {/{moEu#jnaI>'-{?p_ "N(YȳFȒA(郹DVK3_ԜhXfJjtѽʞ@&Jjtoyl_ypdR)@PXUCh PοXQs 9m4#G%-B''7Y 3{[!q4#ɩ96qƂɘ8K ,Zr=̒Uh\EÒYdJMnFU{0oK^05 aghΖgOL#OBvH8'$1fALJ ]bH@AfШ}nꗌ7$5@, YL3ͭUJsI$7k 8rպ=Ix&U*: l#IPVd[Ul}*@hΰ' ɟl;cٓuaɨKK&T-4vd9)Y^[$%ife ݑMӛv6OPPua3Ʃ8gKmL/vnXL9876dHld3fJ'neZuOJ&/ mJY7٤)#%#l]d %FUUyt)WdɸqbA[eڱPv' 4 ;?2*&-#W=z>y䓥fXu};d}dFbeH!.m) ?.r)/m^n>Aݻ<ץ|7|OI>+m_IENDB`DdJ ' S &Ag5%b(@0I[ν&|n@0I[ν&PNG  IHDRFΔ0PLTEletRNS0JbKGDH cmPPJCmp0712OmCIDATx E;An?'R~Z+jZkĖ-} ߣwZZ{j^Dst,519Qj蝣Ca@eԒ굽і2حFkp(z@ɅE3^؂ZDu.evKd~8Jꢰ5=qWFBy1RL{%*/։ž[rFYD BfTuA= Jcjj(;{ZK}yR }Pw^ $[>:++Ž,˙\ٰ7*Z.6VjVjVj@=>P=My[?l:jzCSoamxswj&#B/) H$E:u6k¦"{Kj1S4֣3+jZcttL_ZdPGmyjrHvK8~m6c{)SU32ZsꄰL.A=UA;-3PoQ7^,SjVjL=;~Aqkr@eGݷoHC2םuô ^#5b/ #8:&8<.0g?/̿}w5G+}[Nbqq*&5ySN[}mr:SB ʚoPߺ0y%|eBzj| lS]z oC-Qb,`9@l9L4ht_okX4˖>W_.r uS#e.;hjM1JJwn͡off>ԵZ"vTJJ·b Zo'zFmϙtMpVj 2L)Sj9rLR1c2 4IENDB` Dd J ( S &Ag6&b iRCE쳥z ?^|nV iRCE쳥z ?PNG  IHDR#Ǘ PLTEKXtRNS0JbKGDH cmPPJCmp0712OmIDATxn8`DRw{Uir>lf#ak IZ5ǝ?'㨛̒}G2)#Fg 891ۏ˨`HQǻBE"^lgw]JxeRmKv)^)PB|^<ͺSxnFÈ^]A6p<,xKP+R&@9 ~r/v}x&\()*2mdMΖ׌wS)Sㅴ2WjU#F .o:=ɫ}|N|Cozvo:}*T|ы_ּ0{"קNAxij;<>iju xQj;ZQ;~‧Ӻ Vyjoc|,>8>^3oi^?Jz;ɽ@`_|)w[4z:-ͼ㛤T/K-y_땏{#νT3!uw?B+ P\80É0^n{u.{룡ޕf^M΍<Oo{*flBƛ%/y~گOi^Z?K={] .|^>@I5i&X{ja-gs=uJ$oiۛ¨m[gѓg4SyA/.;E]?]{y*yKO?˫bY۽3}|E+-Zo!σgFoW>5 :y&3Y?~:y{З̞47oc}xVOϼ~Ň7>3/zUّNx|$3OϿx=Q^pio#^[_򒗼%/y=uɥٍH!9o QB KXع^>ZBasDŽUahTNi ' 5^ʺ%tiǃ6!F4^Vz#՟-%䖼%/yPΣ2IENDB`"Dd4 J ) S &Ag7'ba|a65pY%9`|nXa|a65pY%9PNG  IHDRP PLTEKXtRNS0JbKGDH cmPPJCmp0712OmIDATxK*P, 5KRTud^]峍ؤE~;2aZCf9OdhmV76H:3LAJCTY\ 4 ސIϑ. g\Ay%ԨFh ̈U $֝2 IXZV^=RBw(KSjY2$B׀r]@ yg Qoa fer6'1) WjQN^6艏ur⢫yCВҸm]H\pn׸$FS180qJV^:FĐBlUGǪ;B4gsYC@^iʨk`jCRg"ͽ=( =lߒaϴp̈́\1|lmxAsۯ8vݿʿIiHؕ@7- Crެqpa)OQ}hrKĚMy3 ghr~z<\W"Qm=l a NKb:uXꐩn3333c:@l{:ؘcdo#C 7f;deŹw}|~|;e-o +of@1!˛6F_g<afnhnٲJEQls/_ 㒑z*iY1!&Q~ y ݹ1k @uݟܘߟ+eI(d+P_=9?]әn5@1qky!1[vCM1x Le!Zf&xV9Ųϥ:x M F'x< Q4F'x65 ȇT&`0x ߓzޟ at`5 O+ɴCcQOUm_~}|w78ޠ9%m$n/lW{?&Gs[]~ 3͌u3=X.|WF~(}oL(|Kٹq^xBy 0X:a絇q6aAIJ8P̅| 3B,y΃kMq:^q1dLj^ 5[wqe"ρ !"/.ll000b'`WiIENDB`Dd J * S &Ag8(b9Jv3cX)|n Jv3cX)PNG  IHDRI PLTEKXtRNS0JbKGDH cmPPJCmp0712OmxIDATx m~Jqsj}}x)kC I+); 2mԡoN;y*,I\+y,JK6(dzX'^`-#x~X2,#<щK|,/4Ǖ)0R""YzV ɼ~ ZHL(\uʓeg'p+V\f3H2IOry'fY=ͲzfY5C僓`Z̥|z7Z廓>yPlXyxkaEa\>,kaMa|oYȐע)+mĬuK-==e~0O|;<ß/:HL4+ ~]T]/Jmw[xN8[bֈ.:'gDxsmyLKtQM2uOo#|OTų&.u+X5l钪ylRY$ӹ o)YR_~<}.}o{\N]%y26p,J<_*)ƢiR*ph*W@* Strong5\4 @4 Footer  !.)@!.  Page NumberB^@2B  Normal (Web)dd[$\$PK![Content_Types].xmlj0Eжr(΢Iw},-j4 wP-t#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi};~@(Hu* Dנz/0ǰ $ X3aZ,D0j~3߶b~i>3\`?/[G\!-Rk.sԻ..a濭?PK!֧6 _rels/.relsj0 }Q%v/C/}(h"O = C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xml M @}w7c(EbˮCAǠҟ7՛K Y, e.|,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+& 8PK!Ptheme/theme/theme1.xmlYOo6w toc'vuر-MniP@I}úama[إ4:lЯGRX^6؊>$ !)O^rC$y@/yH*񄴽)޵߻UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\|ʜ̭NleXdsjcs7f W+Ն7`g ȘJj|h(KD- dXiJ؇(x$( :;˹! I_TS 1?E??ZBΪmU/?~xY'y5g&΋/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ x}rxwr:\TZaG*y8IjbRc|XŻǿI u3KGnD1NIBs RuK>V.EL+M2#'fi ~V vl{u8zH *:(W☕ ~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4 =3ڗP 1Pm \\9Mؓ2aD];Yt\[x]}Wr|]g- eW )6-rCSj id DЇAΜIqbJ#x꺃 6k#ASh&ʌt(Q%p%m&]caSl=X\P1Mh9MVdDAaVB[݈fJíP|8 քAV^f Hn- "d>znNJ ة>b&2vKyϼD:,AGm\nziÙ.uχYC6OMf3or$5NHT[XF64T,ќM0E)`#5XY`פ;%1U٥m;R>QD DcpU'&LE/pm%]8firS4d 7y\`JnίI R3U~7+׸#m qBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCM m<.vpIYfZY_p[=al-Y}Nc͙ŋ4vfavl'SA8|*u{-ߟ0%M07%<ҍPK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 +_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!Ptheme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK] ' D $$$'!&,/ ^(//!GS\^  ` P R X D F PRS68;DF68  z|}\^aFH_CEO.0'),.S U !!=!!!^""""l#n##$$3$$$M%%%+&&&'XCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC  '!!8@0(  B S  ? introductionKarnaughexampleproblemAdj'> '%-:B 'DL4<bj ('''''''''''V X TV^|&&~'''''''''''''33333333x4\ &&&&'''''''''''2>y y 44&&'<6,x "z9IjPvJب^`CJOJQJo(^`CJOJQJo(opp^p`CJOJQJo(@ @ ^@ `CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(PP^P`CJOJQJo(^`.^`.pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`.^`CJOJQJo(^`CJOJQJo(opp^p`CJOJQJo(@ @ ^@ `CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(^`CJOJQJo(PP^P`CJOJQJo(^`.^`.pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`.<x "IPvJSc fL5w ;/EG  T=XZ` .CcE^1n_8''@'X@UnknownG*Ax Times New Roman5Symbol3. *Cx Arial?= *Cx Courier New;WingdingsACambria Math"qh55!G!G!24''3HX ?2!xx'Karnaugh Maps - Rules of SimplificationmcollegeNatalee Nembhard    Oh+'0dx   , 8DLT\(Karnaugh Maps - Rules of Simplification mcollege Normal.dotmNatalee Nembhard3Microsoft Office Word@^в@FFu@u!՜.+,D՜.+,T hp|  G' (Karnaugh Maps - Rules of Simplification Title 8@ _PID_HLINKSAfaAhttp://www.ee.surrey.ac.uk/Projects/Labview/common/glossary.htmltt  !"$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry FmuData #,1Table,WordDocument.DSummaryInformation(DocumentSummaryInformation8CompObjy  F'Microsoft Office Word 97-2003 Document MSWordDocWord.Document.89q