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Page 1: robertfrench.org*0/ 1 24365. 2 2(701 / 805 9 3 :,*,; < 2 / =2. 9,/?>4/ @0ab1; / 8,2 c d e / 5 2 1 < a e0d 8,f < 8,/ 8,fa 80= g.; @,:,2 143,5 8h5 < 8ji a 1 2 a e 7,:

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< 8JI�A 1 2 < A E 7,: E K0E E ;�/ 8�2 . C 2 9,/- / LB:,< 1 / ;�/ 862 M C . 1�2 90/

>(/ FB1 / / . CN AB5 9,/ E . 1 .BC 365 < / 805 /4< 8�G . ;�@,:,2 / 14365 < / 805 /?AB80= D 8,FB< 8,/ / 1 < 8,F

A 2(2 9,/O�P 3,3 P G$Q4R(3 D$S�S 3�T U43 S T S R S�DWV 7 S�D G$Q(U V4XYV?Z4[

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3�< FB80AB2 :01 / .BC$P :,2 9 . 1 d>(/ @0A 1 2 ;�/ 8,2 . C$D�E / 5 2 1 < 5 A E0D 8,F�< 80/ / 1 < 8,F�A 80=�G . ;�@,:,2 / 1?365 < / 805 /

O A +�e6]�fH] ^B^B_G�/ 1 2 < K / =�*,+Hd

S 9 . ;�A�M(7$c,g48,< FB9,2 f \ 1 cI�1 .BC / M M . 1 f0>4/ @HA 1 2 ;�/ 8,2 .BC$D�E / 5 2 1 < 5 A EHD 8,FB< 8,/ / 1 < 8,F�AB80=�G . ;�@,:,2 / 1?365 < / 805 /

S 9,/ M < M(3�:,@0/ 1 h6< M . 1P 5 5 / @,2 / =�*0+0d

X / . 80A 1 = P c Z(. : E =G�90AB< 1 ;�A 8if0>(/ @0A 1 2 ;�/ 8,2�G . ;�;�< 2 2 / / . 8�R�8H=6/ 1 F�1 AB=6:0AB2 / S 90/ M / M

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=6< 2 < . 80M cH¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸?¸a¸4¸Å] �¹6c ] S 9,/aA E 2 / 1 80A 2 / � M E A 802$AB1 5 9,< 2 / 5 2 :01 /Bc�¸4¸a¸4¸a¸4¸a¸?¸?¸?¸4¸a¸4¸a¸4¸a¸?¸?¸?¸?¸?¸Ç] ^¹6c e S 9,/?; . =6: E /?@ . M < 2 < . 80M(A C 2 / 1�@ E AB5 / ;�/ 862 c�¸?¸a¸4¸a¸4¸?¸?¸?¸?¸?¸a¸4¸a¸4¸a¸4¸�eBù6c ¹ S 9,/ K 8HA E AB1 1 A +�A C 2 / 1�1 . :,2 < 8,F,ci¸4¸a¸4¸a¸?¸?¸?¸?¸?¸?¸?¸4¸a¸4¸a¸?¸?¸?¸?¸?¸?¸?¸Ìe�ù6c » S 9,/?90AB80=6� . @,2 < ;�< � / =�A 1 1 AB+�A C 2 / 1�1 . :,2 < 8,F0c�¸a¸4¸a¸4¸?¸a¸4¸a¸4¸a¸4¸a¸4¸a¸4¸�¹B_»,c ] S 9,/ . 1 < F�< 80A E�C . :01 � *,< 2�1 < @,@ E /$5 A 1 1 +�AB=0=6/ 1$AB1 1 A +6f AB80=�2 9,/(A 1 1 A +aA C 2 / 1�¹6f Ù ��_

. @,2 < ;�< � A 2 < . 8)< 2 / 1 AB2 < . 80M c$¸4¸a¸4¸?¸?¸?¸?¸?¸a¸4¸a¸4¸a¸4¸?¸?¸?¸?¸?¸a¸4¸a¸4¸a¸4¸�¹B^»,c e½T 2 / 1 A 2 < . 8�h,M c65 . M 2 C . 1$2 9,/ C . :,1 � *,< 2�1 < @0@ E /45 A 1 1 +�AB=,=6/ 1 f,M 2 A 1 2 < 80F�2 / ;�@0/ 1 A �

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3 .�C AB1i2 9,/�M 9 . 1 2 � 2 / 1 ;u;�/ ; . 1 < / M02 9HA 2i90A h6/Y*0/ / 8?:0M / =42 . M 2 . 1 /$2 9,/�< 8,2 / 1 ;�/ =6< A 2 /�1 / M : E 2 M . CA C .�E =6/ =aA 1 1 AB+?90A h6/Y*H/ / 8 E / C 2i:,80=6/ M 5 1 < *H/ =Hc S 9,/ +a5 . : E =a*H/$< ;�@ E / ;�/ 8�2 / =4:0M < 8,F?M 2 AB80=,A 1 =-(P(O b�< 2 9)2 9,/aAB=,=61 / M M4=,/ 2 / 1 ;�< 8,/ =�*,+�2 9,/4@HA 1 2 < 5 : E A 1�@,90A�M / . C =,A 2 A�� . b?f6*,:,24A�;�:05 9; . 1 /4:0M / C : E AB1 1 A 8,FB/ ;�/ 802�< M�@ . M M < * E /�c S 9,/?M 9 . 1 2 � 2 / 1 ;�;�/ ; . 1 +�5 A 8JAB5 2 :0A E E +a*H/(h6< / b�/ =ABM�A4M / 2 . C =6/ E A + E < 8,/ M f b(< 2 9 . 8,/$=6/ E A + E < 8,/ C . 1Y/ AB5 9 . C 2 9,/C�s­ . :,2 @0:,2 M . C A4@,1 . 5 / M M . 1 c P 8/ Ï AB;�@ E / . C 2 9,< M�< M�M 9 . b(8�< 8�7Y< FB:,1 /(e6c Ã6c S 9,< M K FB:,1 /(M 9 . b(M�AaM < 80F E / � @01 . 5 / M M . 1�/ ;�: E A 2 < . 8. C 2 9,/4»iæ�»�A 1 1 A +�b�/�< 802 1 . =6:05 / =�< 8�7Y< FB:,1 /4e6c ]Bc�7 . 1�/ A�M / . C =6< M 5 :0M M < . 8if62 9,/(@01 . 5 / M M . 1$< 82 9,< M K FB:,1 /�= . / M�8 . 2�90A h6/4A 8J< 8,2 1 < 8HM < 5(=6/ E AB+Bc

S 9,/ E / 8,F�2 9 . C A)F�< h6/ 8�=6/ E AB+ E < 80/�5 A 8�*0/�/ ABM < E +�=6/ 2 / 1 ;�< 8,/ =Hc�T C 2 9,/�I D M?< 8�A 8. 1 < F�AB;�<6A 1 1 AB+4AB1 /�8,:0;a*0/ 1 / =�< 8�A(1 ABM 2 / 1 � M 5 AB8 C ABM 9,< . 8if�ABMYM 9 . b�8?< 8a7Y< F�:,1 /$e6c ^6f 2 90/ E / 80FB2 9. C A�=6/ E A + E < 8,/?*0/ 2 b$/ / 8�2 9,/ . :,2 @,:,2 . C�. 80/aI D A 80=J2 9,/?< 80@,:,2 . C A 8 . 2 9,/ 1(< M(M < ;�@ E +�2 9,/=6< � / 1 / 8H5 /(< 8J2 90/(8,:,;�*0/ 1 M . C 2 9,/42 b . I D M c V :,1�M A ;�@ E /4AB1 1 A +�1 / LB:,< 1 / M�2 b . =6/ E A + E < 8,/ M f. 8,/ .BC$E / 8,FB2 9�»�A 80= . 8,/ .BC$E / 8,FB2 9��,c S 9,/ E / 8,FB2 9 .BC 2 9,/�=6/ E AB+ E < 8,/ M(< M4AB@,@,1 .BÏ < ;�AB2 / E +@,1 . @ . 1 2 < . 80A E 2 . 2 9,/�b�< =62 9 . C 2 9,/�A 1 1 AB+�f b�9,< 5 9�< MY5 . 80M < M 2 / 8,2Yb�< 2 9 . :01�/ AB1 E < / 1 . *0M / 1 hBAB2 < . 82 90A 2 . 8 E +�b�< =62 9,b�< M / C .BE =6< 8,F�1 / L�:,< 1 / M�/ Ï 2 1 Aa;�/ ; . 1 +�c

] ¹

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45Delays

Inputs

Outputs

Multiplexers

Processor Program

7Y< F�:,1 /ae6c Ã,d P M < 8,F E / � @,1 . 5 / M M . 1(/ ;�: E AB2 < . 8 . C Aa»Yæ�» . 1 < F�AB;�<YA 1 1 A +�:0M < 8,F�=6/ E A + E < 8,/ M c

0 1 2 3

4 5 6 7

8 9 10 11

12 13 14 15

7Y< F�:,1 /ae6c ^,d S 9,/41 A�M 2 / 1(M 5 AB8J8,:,;�*0/ 1 M C . 1(A�»Yæ�» . 1 < F�AB;�<YA 1 1 AB+�c

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ACB D8B ®©¯ k(v?q8M?x$t2¤"jlk�q8M�o w0o k(q4{

V 805 /4b(/4M / /?2 90A 24=6/ E A + E < 8,/ E / 8,FB2 90M(5 AB8J*0/�5 A E 5 : E AB2 / =�:0M < 8,F�1 ABM 2 / 1 � M 5 AB8�8,:,;�*0/ 1 M fBb�/5 A 8 M / /�9 . b�2 90/�AB1 1 A +�*0/ 9HA h6/ M?A 2�< 2 M�* . :,80=,AB1 < / M c�R(M < 8,F�7i< FB:01 /)e,c ^�A�M�AJF�:,< =6/BfYb�/M / /�2 90A 2�I D _2° M . :,2 @,:,2 M�AB1 / C / =�2 . I D Ma»�AB80=��6c XH.6. �6< 8,F�A 2�2 9,/�A 1 1 AB+ C :01 2 90/ 1 fYb�/M / /)2 90A 2�I D ¹�;�:HM 2a2 A E ��2 . I D Ù�AB80= Ã6c S 9,:0M�2 9,/)*0/ 90ABh�< . 1 .BC 2 9,/ E / C 2�AB80=l1 < FB9,2/ =6FB/ M�5 A 8 8 . b�*0/�:,80=6/ 1 M 2 .�. =Hf�AB80= < M�=61 A b�8 < 8 7Y< F�:,1 /�e6c ] _6cWÁW9,/ 8W=,A 2 A�� . b(M . �2 9,/�1 < F�9,2490A 80=lM < =6/ . C 2 9,/)A 1 1 AB+�fH< 2?/ M M / 8,2 < A E E + � M �6< @0M�AB9,/ AB=,� . 8,/)5 E . 5 ��5 +,5 E /�c S 9,< M@,1 . h6< =6/ M0< 8,2 / 1 / M 2 < 80F�@ . M M < *0< E < 2 < / M C . 1Y2 < ;�/ � = . ;�A < 8?;�: E 2 < @ E / Ï < 8,F,f A 80=a< Mi=6< M 5 :HM M / =?*,1 < / �0+< 8�G�90A @,2 / 1?�6caQ . b�/ h�/ 1 f C . 142 9,/�; . M 24@0AB1 2?2 90/ M /a* . :,80=,A 1 +�5 . 80=6< 2 < . 80M4A 1 /�8 . 2(< 8�2 9,/M 5 . @0/ . C 2 9,< M$2 9,/ M < M c

7Y< F�:,1 /�e6c ] _6d S 9,/�< 8,2 / 1 5 . 8,8,/ 5 2 < . 8 . C A�»Yæ�» . 1 < F�A ;�<�A 1 1 A +)< 805 E :0=6< 8,F�* . :,80=,A 1 +�5 . 80=6< �2 < . 80M c

] �

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��� ±³² � ��´��?�sµ.¶"� ���a�!�� ����������� �������

P(E E 2 9,/?/ Ï A ;�@ E / M�2 90AB2?90A h�/?*0/ / 8�@,1 / M / 8,2 / =)M .�C AB1 fHAB80=�< 8 C A�5 2?A E E 2 9,/�/ Ï A ;�@ E / M(2 90A 2b�< E E *0/�M / / 8 E A 2 / 1 fH5 . 802 A < 8�2 b . � =,< ;�/ 80M < . 80A EY. 1 < F�A ;�<�A 1 1 A +,M c S 9,/ M /�A 1 /�/ Ï @ E . 1 / =J9,/ 1 /M < ;�@ E +�*0/ 5 AB:0M /a2 9,/ +)AB1 /?2 9,/?/ ABM < / M 2(2 . A 80A E +6� /�c�Q . b$/ hB/ 1 f6A E E 2 9,/?@ . < 8,2 M$;�AB=,/?< 8)2 9,< M5 90A @,2 / 1�A E M . AB@,@ E +�2 .�. 1 < F�A ;�<iA 1 1 A +,M$b�< 2 9); . 1 /42 90A 8J2 b . =6< ;�/ 80M < . 80M c�T 8�2 9,/ M /?5 ABM / M f2 9,/ 1 /4< M . 8,/?=6< ;�/ 80M < . 8)2 90A 2(5 A 8 C .�E =)=6/ @,2 9,b�< M /�f�AB80=)2 9,/?1 / M 2(5 AB8 C .BE =)b�< =62 90b�< M /Bc

��� ·¹¸ ´º%��"!������)�Î����������� ����������� ��������»

T 2(< M�/ h6< =6/ 862 C 1 . ;ì2 9,/�A * . h�/?=6< M 5 :0M M < . 8J2 90AB2?5 . ;�@,:02 A 2 < . 80A EY. 1 < F�AB;�<�90ABM4A�8,:,;�*0/ 1 .BCM / 1 < . :0M�=6< M AB=,hBAB8,2 A FB/ M c�7 . 1�/ Ï A ;�@ E /�f < C M < ;�@ E /�f K 8,/ � F�1 A < 8,/ =�@01 . 5 / M M . 1 M$AB1 /(:0M / =ifB/ < 2 9,/ 1A E . 2 .BC 90A 1 =6b(AB1 / . 1 E . 8,Fl=6/ E AB+ E < 8,/ M�A 1 /J1 / L�:,< 1 / =l2 . / Ï / 5 :,2 /)Al5 . ;�@ E / Ï @,1 . FB1 AB;)cT 2�< M�< ;�@,1 AB5 2 < 5 A E 2 . < ;�@ E / ;�/ 862�A 8 . 1 < F6A ;�<4AB1 1 A +l< 8WM < E < 5 . 8W*0/ 5 A :0M /J2 9,/ E . 8,F =6/ E A +E < 8,/ M�1 / LB:0< 1 / =�A 1 /?8 . 2(AB1 / AB� / ö�5 < / 8,2�b(9,/ 8)< ;�@ E / ;�/ 862 / =�:0M < 8,F�M 2 A 80=,AB1 =)2 / 5 9,8,< L�:,/ M ciT 8AB=,=,< 2 < . 8if0/ h6/ 8�b�< 2 9J2 9,/?;�A Ï < ;�:0;�8,:,;�*0/ 1 . C :0M / C : E @,1 . 5 / M M . 1 M4ABh�A < E A * E /Bf�2 9,/�M +,M 2 / ;b�< E E 90A h�/?A�9,< FB9 E A 2 / 805 +�c$7Y< 80A E E +�f�2 9,/�M +,M 2 / ;�M(2 90A 2(90ABh�/4*0/ / 8�5 90AB1 AB5 2 / 1 < � / =�9,/ 1 /�5 AB8. 8 E +J1 :,8�@,1 . F�1 A ;�M?2 90A 2?5 A 8�*0/a< ;�@ E / ;�/ 862 / =)b�< 2 9 . :,24< 80=6/ 2 / 1 ;�< 80A 2 /a1 / 5 :,1 M < . 8ifiM < 805 /2 9,/a=,A 2 A�� . b�;�:0M 2$*0/a5 A :0M A E c

Q . b�/ h�/ 1 f . 1 < F�A ;�<690ABM�A(8,:,;�*0/ 1 .BC AB=6h�A 8,2 ABFB/ M c V 1 < F�AB;�<,M +,M 2 / ;�M�A 1 /$/ A�M +a2 .4E A +. :,2(AB80=�b�< 1 /Bc S 9,/ 1 /4< M$A�8,/ A 1 E +�@0/ 1 C / 5 2$@,1 . 5 / M M . 1 � M @H/ / =)2 1 AB=6/ . � f0A�M . @0@ . M / =)2 . ; . M 2@0A 1 A E E / E @,1 . 5 / M M < 8,F4AB1 5 9,< 2 / 5 2 :01 / M,b(9,< 5 94FB/ 2i* . FBFB/ =a= . b�8?< 8a5 . ;�;�:,8,< 5 AB2 < . 845 . M 2 MYA�MH2 9,/8,:,;�*0/ 1 . C @,1 . 5 / M M . 1 M�< 805 1 / ABM /�c S 9,/ 1 /$< MY/ Ï 5 / E E / 862i2 9,1 . :,F�9,@,:,2�b�9,/ 8�/ 8 . :,F�9�@,1 . 5 / M M . 1 M

] ¾

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A 1 /(A h�AB< E A * E /BciI�1 . F�1 A ;�M�A 1 /(< 80=6/ @0/ 80=6/ 8,2 .BC 2 90/$8,:,;�*0/ 1 . C @,1 . 5 / M M . 1 M�A h�AB< E A * E /�A�M E . 8,FABM(M :6ö)5 < / 862 E + E . 8,F�=6/ E A + E < 8,/ M�5 A 8)*0/?5 . 80M 2 1 :05 2 / =Hf�AB80=�8,/ / =�8 . 2$*0/41 / 5 . ;�@,< E / =�ABM�2 90/8,:,;�*0/ 1 . C @,1 . 5 / M M . 1 M$5 9HA 8,FB/ M c P 8H=�5 . ;�@ E / Ï @,1 . * E / ;�M�5 A 8�*0/�@0/ 1 C . 1 ;�/ =ab(< 2 9�A�M E < 2 2 E /ABM4A�M < 8,F E /4@,1 . 5 / M M . 14< C 8,/ 5 / M M AB1 +�c

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�Çî�êìï"�l� ä½¼

���¾� ï Ý í Ý � â ß4� ä ���¾� ï ã ��ê�� Ý �õ��êìí

� ä Ý�â ê:� Ý

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V 8,/ . C 2 9,/�@,1 < ;�A 1 +J@,1 . * E / ;�M�b�< 2 9�A 8 . 1 < F�AB;�<�M +,M 2 / ;ì< M4A�M M < FB8,< 8,F C :,805 2 < . 80M(2 . / A�5 9. C 2 9,/JI D M)M . 2 90AB2�A�2 ABM �l5 A 8W*0/)@0/ 1 C . 1 ;�/ =�/ ö)5 < / 862 E +Jb(< 2 9WA�;�< 8,< ;�A E A ; . :,802 . C90A 1 =,b(A 1 /�c)3�2 AB80=,A 1 =l5 . ;�@,< E / 142 / 5 9,80< LB:,/ M45 AB8�*0/�:0M / =�2 . F�/ 8,/ 1 A 2 /�=,AB2 AJ� . b�FB1 A @,9HMC 1 . ;�5 . ;�@,:,2 / 1 E A 8,F�:0A F�/ M f�*,:,2J5 1 / A 2 < 8,F�A 8 . 1 < F6A ;�<4AB1 1 A + C 1 . ;"2 9,/ E . F�< 5 C :,805 2 < . 80M@,1 . =,:05 / =�< M$A�=6< ö)5 : E 2�@,1 . * E / ;)c�T 8);�AB8,+ab4A +6M�< 2�< M$AB80A E . F . :0M�2 . 2 9,/(F�/ 8,/ 1 A E < � / =�2 b . �=6< ;�/ 80M < . 80A E / E / 5 2 1 < 5 A E 5 < 1 5 :,< 2 E A + . :02$@,1 . * E / ;¾� * ¡ �2¡�2 9,/aAB:,2 . ;�A 2 < 5(1 . :,2 < 80F . C b�< 1 / M . 8A�@,1 < 8,2 / =�5 < 1 5 :,< 2�* . A 1 =.� fH*,:,2(< 2(< M(M :,ö�5 < / 8,2 E +�=,< � / 1 / 8,2�2 90A 245 < 1 5 :,< 2 E AB+ . :,2(A E F . 1 < 2 9,;�MA 1 /(8 . 2�=,< 1 / 5 2 E +?A @,@ E < 5 A * E /�c S 9,/$@,1 . * E / ; . CHK 80=6< 8,FaAB8 . @,2 < ;�A E @ E AB5 / ;�/ 8,2YAB80=�1 . :,2 < 8,F< M�5 . 80M < =6/ 1 / =�2 . *0/aU4I�� 5 . ;�@ E / 2 /�c

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=º� �?¿ ´�������&_´�� ���a&(�����$�

S 9,/�=6/ M 2 < 80A 2 < . 8�A 1 5 9,< 2 / 5 2 :,1 / C . 1)2 9,/�5 . ;�@0< E / 1�@,1 / M / 8,2 / =l< 8W2 9,< M�2 9,/ M < M�b�< E E *0/�2 9,/A E 2 / 1 80A 2 / � M E A 8,2a8,/ 2 b . 1 ��;�/ 8,2 < . 8,/ =�*01 < / �0+�< 8WG�9HA @,2 / 1�e6cWT 2�< M�M 9 . b�8 A F6A < 8W< 8 7Y< FB�:,1 /�¹6c ]Bc S 9,< M�A 1 5 9,< 2 / 5 2 :,1 /)b4ABM)5 9 . M / 8�@01 < ;�A 1 < E + C . 1J< 2 M)M < ;�@ E < 5 < 2 + c S 9,/lM < ;�@ E / 1 f:,8,< =6< 1 / 5 2 < . 80A E � M E A 8,2�AB1 5 9,< 2 / 5 2 :,1 / . 1 < FB< 80A E E +)< 8,2 1 . =6:05 / =�< M�8 . 24:0M / =J*0/ 5 AB:0M /�< 2(< M�; . 1 /=6< ö�5 : E 2�2 . 1 . :,2 /a@,1 . @H/ 1 E +6f6A E 2 9 . :0FB9�G�9,:0AB8,F�90A�M4M 9 . b�8)2 90AB24< 2�< M�@ . M M < * E /a2 . 5 . 8,h�/ 1 22 9,/�:,8,< =,< 1 / 5 2 < . 80A E � M E AB8,2�A 1 5 9,< 2 / 5 2 :,1 /)< 8,2 . 2 9,/�A E 2 / 1 80A 2 / � M E A 802�AB1 5 9,< 2 / 5 2 :01 /�A�M M :,;�< 8,F* . :080=,A 1 +J5 . 80=6< 2 < . 80M(A 1 /?< F�8 . 1 / =� � � c

7Y< F�:,1 /?¹6c ]�d S 9,/?A E 2 / 1 80A 2 / � M E A 802�A 1 5 9,< 2 / 5 2 :,1 /Bc

=º� =³¿ ´��ÁÀ��)�J��� ��£�Í ������� �s´��

G�9,:0AB8,F0 ¹ �4=6/ h�/ E . @0/ =lA�@,1 . 2 . 2 +6@0/)1 . :,2 < 80FlM +,M 2 / ; C . 1)A�2 9,1 / / � =6< ;�/ 80M < . 80A E�. 1 < F�AB;�<A 1 1 AB+?:HM < 8,F�A4� .6. =6< 8,F�A E F . 1 < 2 9,;�b�< 2 9�*0AB5 �62 1 AB5 �6< 8,F0c S 90< M�b4ABM�:0M / =�2 . @ E A�5 /(A 80=�1 . :,2 /

] ^

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A�ÁlA E E AB5 /?2 1 / /�AB=,=,/ 1 c?Q�/ 1 /ab�/a@,1 . @ . M /�AB8�A E F . 1 < 2 9,; C . 14@ E AB5 < 8,F E . FB< 5 C :,805 2 < . 80M(AB80=1 . :,2 < 8,F�*H/ 2 b$/ / 8�2 9,/ ;�< 8)2 b . =,< ;�/ 8HM < . 80M$b�< 2 9 . :,2�2 9,/?8,/ / = C . 1�*0AB5 �62 1 AB5 ��< 8,F0c

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V 8,/a;�AB< 8�5 . 8H5 E :0M < . 8J5 A 8J*0/�=61 ABb�8 C 1 . ;�2 9,/ M /?F�1 A @,90M c P M�2 9,/a< 8,< 2 < A E 2 / ;�@0/ 1 �A 2 :,1 /�< 805 1 / ABM / M f0AB80=J2 9,/�AB8,8,/ A E < 8,F)< M(A E E . b(/ =�2 . 2 A �6/4@ E A�5 / . h�/ 1$; . 1 /a< 2 / 1 AB2 < . 80M f02 9,/1 / M : E 2 AB8,2�M +,M 2 / ;�< MY; . 1 / . @,2 < ;�< � / =ic S 9,/ K 1 M 2$AB8,8,/ A E < 8,F�M 5 9,/ =6: E /�f 2 9,/(1 / M : E 2 M . C b�9,< 5 9A 1 /aM 9 . b�8)< 8)7Y< FB:01 /4»0c e,f,= . / M$8 . 24A E E . bWA 80+�M 9,< C 2 M$2 . A � b . 1 M / ��M +6M 2 / ;Jf6AB80=�2 9,:0M�2 9,/M +,M 2 / ;�5 AB8,8 . 2�/ M 5 A @0/ C 1 . ;�2 9,/ E . 5 A E ;�< 8,< ;�A?< 2$< M�< 8,< 2 < A E E +�@ E AB5 / =�< 8ic�Q . b$/ h / 1 f�ABM$2 9,/M +,M 2 / ;�*0/ 5 . ;�/ M$; . 1 / � / Ï 5 < 2 / =,��=6:,1 < 80F�2 9,/?*0/ F�< 8,80< 8,F . C 2 9,/aA 8,8,/ A E < 8,F�@,1 . 5 / M M f0ABM�< 87Y< F�:,1 /�»,c Ù6fi< 2?5 A 8�/ M 5 A @0/ C 1 . ; E . 5 A E ;�< 80< ;�A�AB80= C A E E < 8,2 . A)*H/ 2 2 / 1 E . 5 A E ;�< 8,< ;�A . 1 fb�< 2 9�M . ;�/ E :05 �Hf0A)F E . *0A E ;�< 8,< ;�A6c S 9,< Ma< E E :0M 2 1 A 2 / M(2 9,/�@,1 < ;�A 1 + C / A 2 :,1 / . C M < ;�: E A 2 / =A 8,80/ A E < 8,F,f�2 9,/4A *,< E < 2 +42 . A h . < = E . 5 A E ;�< 8,< ;�A(*,+a/ Ï 5 < 2 < 8,F42 9,/4M +6M 2 / ;�A 80=�2 9,/ 8�A E E . b(< 8,F< 2�2 .�� 5 .�.�E ��FB1 AB=6:HA E E + . h6/ 1�A E . 8,F�@0/ 1 < . = .BC 2 < ;�/Bc

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0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

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23

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25

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42

43

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47

48

49

50

51

52

53

54

55

56

-2 -1 0 1 2 3 4 5 6 7 8 9 10

HA HA HA HA

HA

OR

HA

OR

HA

OR

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

-2 -1 0 1 2 3 4 5 6 7 8

HAR HAR HAR HAR

HAR

OR

HA

OR

HA

OR

7Y< F�:,1 /�»,c ]�d S 9,/ . 1 < F�< 80A EiC . :,1 � *,< 241 < @,@ E /a5 A 1 1 +�A�=,=6/ 1?AB1 1 A +6f,AB80=�2 9,/�A 1 1 A +JA C 2 / 1?¹6f Ù ��_. @,2 < ;�< � A 2 < . 8)< 2 / 1 AB2 < . 80M c

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Page 48: robertfrench.org*0/ 1 24365. 2 2(701 / 805 9 3 :,*,; < 2 / =2. 9,/?>4/ @0ab1; / 8,2 c d e / 5 2 1 < a e0d 8,f < 8,/ 8,fa 80= g.; @,:,2 143,5 8h5 < 8ji a 1 2 a e 7,:

|R0S |R

20|R

40|R

60|R

80|R

100S|T160

|T180

|T200

|T220

|T240

|T260

|T280

Simulated Annealing: Start temp 1.000000, Iters 100, Mult 0.990000

Trial number

Cos

t

7Y< F�:,1 /(»,c e,d�T 2 / 1 A 2 < . 8�h,M cB5 . M 2 C . 1$2 9,/ C . :,1 � *,< 2$1 < @,@ E /(5 A 1 1 +�AB=,=6/ 1 f6M 2 A 1 2 < 8,F?2 / ;�@0/ 1 A 2 :,1 /]Bf,2 / ;�@0/ 1 A 2 :,1 /?;�: E 2 < @ E < / 1(c ^�^6fY] _B_�< 2 / 1 A 2 < . 80M c

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Page 49: robertfrench.org*0/ 1 24365. 2 2(701 / 805 9 3 :,*,; < 2 / =2. 9,/?>4/ @0ab1; / 8,2 c d e / 5 2 1 < a e0d 8,f < 8,/ 8,fa 80= g.; @,:,2 143,5 8h5 < 8ji a 1 2 a e 7,:

|R0S |R

60|R

120U |R180V |R

240W |R300S |R

360X |R420U |R

480V |R540W|T160

|T180

|T200

|T220|T240

|T260

|T280

|T300

Simulated Annealing: Start temp 10.000000, Iters 500, Mult 0.990000

Trial number

Cos

t

7Y< F�:,1 /(»,c ¹,d�T 2 / 1 A 2 < . 8�h,M cB5 . M 2 C . 1$2 9,/ C . :,1 � *,< 2$1 < @,@ E /(5 A 1 1 +�AB=,=6/ 1 f6M 2 A 1 2 < 8,F?2 / ;�@0/ 1 A 2 :,1 /] _,f,2 / ;�@0/ 1 AB2 :,1 /(;�: E 2 < @ E < / 1(c ^B^6f0�B_�_�< 2 / 1 AB2 < . 80M c

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|R0S |R

90|R

180V |R270Y |R

360X |R450Z |R

540W |R630[ |R

720U |R810\|T160

|T180

|T200

|T220|T240

|T260

|T280

|T300

Simulated Annealing: Start temp 25.000000, Iters 750, Mult 0.990000

Trial number

Cos

t

7Y< F�:,1 /(»,c »0d�T 2 / 1 A 2 < . 8�h,M cB5 . M 2 C . 1$2 9,/ C . :,1 � *,< 2$1 < @,@ E /(5 A 1 1 +�AB=,=6/ 1 f6M 2 A 1 2 < 8,F?2 / ;�@0/ 1 A 2 :,1 /eB�,f,2 / ;�@0/ 1 AB2 :,1 /(;�: E 2 < @ E < / 1(c ^B^6fHÙ ��_�< 2 / 1 AB2 < . 80M c

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Page 51: robertfrench.org*0/ 1 24365. 2 2(701 / 805 9 3 :,*,; < 2 / =2. 9,/?>4/ @0ab1; / 8,2 c d e / 5 2 1 < a e0d 8,f < 8,/ 8,fa 80= g.; @,:,2 143,5 8h5 < 8ji a 1 2 a e 7,:

|R0S |R

200S |R400S |R

600S |R800S |R

1000

|T150

|T180

|T210

|T240|T270

|T300

|T330

|T360

Simulated Annealing: Start temp 40.000000, Iters 1000, Mult 0.990000

Trial number

Cos

t

7Y< F�:,1 /(»,c �,d�T 2 / 1 A 2 < . 8�h,M cB5 . M 2 C . 1$2 9,/ C . :,1 � *,< 2$1 < @,@ E /(5 A 1 1 +�AB=,=6/ 1 f6M 2 A 1 2 < 8,F?2 / ;�@0/ 1 A 2 :,1 /»�_,f,2 / ;�@0/ 1 AB2 :,1 /(;�: E 2 < @ E < / 1(c ^B^6fi]Bf _B_�_�< 2 / 1 AB2 < . 80M c

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|R0S |R

200S |R400S |R

600S |R800S |R

1000|R

1200|R

1400

|T100

|T150

|T200

|T250

|T300|T350

|T400

|T450

|T500

|T550

Simulated Annealing: Start temp 55.000000, Iters 1250, Mult 0.996000

Trial number

Cos

t

7Y< F�:,1 /(»,c ¾,d�T 2 / 1 A 2 < . 8�h,M cB5 . M 2 C . 1$2 9,/ C . :,1 � *,< 2$1 < @,@ E /(5 A 1 1 +�AB=,=6/ 1 f6M 2 A 1 2 < 8,F?2 / ;�@0/ 1 A 2 :,1 /�B�,f,2 / ;�@0/ 1 AB2 :,1 /(;�: E 2 < @ E < / 1(c ^B^B¾,fH]�f e��B_�< 2 / 1 A 2 < . 80M c

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|R0S |R

500S |R1000

|R1500

|R2000

|R2500

|R3000

|R3500

|R4000

|T70

|T140

|T210

|T280

|T350

|T420

|T490

|T560

|T630

|T700

|T770

Simulated Annealing: Start temp 70.000000, Iters 3750, Mult 0.999000

Trial number

Cos

t

7Y< F�:,1 /(»,c Ù6d�T 2 / 1 A 2 < . 8�h,M cB5 . M 2 C . 1$2 9,/ C . :,1 � *,< 2$1 < @,@ E /(5 A 1 1 +�AB=,=6/ 1 f6M 2 A 1 2 < 8,F?2 / ;�@0/ 1 A 2 :,1 /Ù _,f,2 / ;�@0/ 1 AB2 :,1 /(;�: E 2 < @ E < / 1(c ^B^B^,f,¹,f ÙB�B_�< 2 / 1 A 2 < . 80M c

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Page 54: robertfrench.org*0/ 1 24365. 2 2(701 / 805 9 3 :,*,; < 2 / =2. 9,/?>4/ @0ab1; / 8,2 c d e / 5 2 1 < a e0d 8,f < 8,/ 8,fa 80= g.; @,:,2 143,5 8h5 < 8ji a 1 2 a e 7,:

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V 8 E +)A C / b�A 1 / ABM .BC 5 . ;�@,< E < 8,F C . 1?5 . ;�@,:02 A 2 < . 80A EY. 1 < F�AB;�<Y90A h6/4*0/ / 8J/ Ï @ E . 1 / =)< 8J2 9,< M2 9,/ M < M c O A 8,+�; . 1 /?1 / ;�AB< 8ic P ; . 8,F�2 9,/ ;�AB1 /Bd

� P 80/ bW2 +6@0/ . C < 8,@,:,2�A 8H= . :,2 @,:,2�M 9 . : E =�*0/4A�=,=6/ =�2 . 2 9,/ E AB8,FB:0ABFB/�f�2 90/47 XYV4P�S �T U Z T U4I�R S A 80=�7 XYV4P�S T U Z�V R S I$R S c S 9,/ M /(5 9HA 8,8,/ E MYb . : E =a*0/ C 1 / /$2 . ; . h�/A 1 . :,80=W=6:,1 < 8,F . @,2 < ;�< � A 2 < . 8if$A 8H=lb . : E =lM .�E h6/)M . ;�/ . C 2 9,/J90A 80=6� . @,2 < ;�< � AB2 < . 8@,1 . * E / ;�M?/ 805 . :08,2 / 1 / =)< 8�M / 5 2 < . 8�¹,c »0c�7Y< Ï / =J@ . M < 2 < . 8lT U(I$R S MaA 80= V R S I�R S Mb�< E E M 2 < E E *0/(80/ 5 / M M A 1 + C . 1�< 8,2 / 1 C AB5 < 8,F?b�< 2 9J/ Ï 2 / 1 80A E 5 . 8,8,/ 5 2 < . 80M f,A 80= C . 1�;�AB�6< 8,FM :,1 /�2 90A 2 . :,2 @,:,2 M�AB80=�< 8,@0:,2 M E < 8,/�:,@lb�9,/ 8�2 b .). 1 < F�A ;�<�AB1 1 A +,M?AB1 /)5 . 8,8,/ 5 2 / =. 142 9,/ . :02 @,:,2 M . C AB8�A 1 1 A +JAB1 / C / =)*0AB5 ��2 . 2 9,/�< 80@,:,2 M�2 . @,1 . =6:05 /�A K 8,< 2 /�M 2 AB2 /;�AB5 9,< 8,/�c

� S 9,/�A 8,8,/ A E < 8,FJM 5 9,/ =6: E /aM 9 . : E =�*0/�/ Ï @0/ 1 < ;�/ 862 / =)b(< 2 9ic S 9,/�M 90A @H/ .BC 2 90/a2 / ;��@0/ 1 A 2 :,1 /�h,M c0< 2 / 1 A 2 < . 8�5 :,1 h�/�5 A 8�*0/�h6/ 1 +)< ;�@ . 1 2 A 8,2(< 8�=6/ 2 / 1 ;�< 80< 8,F�2 9,/�L�:0A E < 2 +. C 2 9,/?1 / M : E 2 A 8,2�M +,M 2 / ;)c

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� P 80:,;a*0/ 1 . C A�M @0/ 5 2 M . C 2 9,/�@ E A�5 / ;�/ 862YAB80=a1 . :,2 < 8,F?A E F . 1 < 2 9,;�5 . : E =?*0/�< ;�@,1 . hB/ =Hc3�@0/ 5 < K 5 A E E +�fB2 9,/(=6/ 2 / 1 ;�< 80A 2 < . 8 .BC F . A E 5 .�E :,;�80M�8,/ / =,M�M . ;�/(b . 1 ��M < 805 /$2 9,/(; . =6�: E / M(A 1 /aM 9,< C 2 / =�2 . ;�AB��/41 .�. ; C . 1�b�< 1 / M$< 8JA�h6/ 1 +a:,80< 8,2 / E E < FB/ 8�2 C ABM 9,< . 8ic

� V 2 9,/ 1)< 2 / 1 A 2 < hB/ . @02 < ;�< � A 2 < . 8W;�/ 2 9 . =,MJM 9 . : E =W*0/�< 8,h�/ M 2 < F6A 2 / =Hc�7 . 1)/ Ï AB;�@ E /BfFB/ 8,/ 2 < 5�A E F . 1 < 2 9,;�M� Ù�f�Ã,f$]B]�f�e »!��90ABh�/�@,1 . hB/ 8�2 9,/ ;�M / E h�/ M?b . 1 2 9,b(9,< E /�< 8�;�A 8,+=6< � / 1 / 802�AB@,@ E < 5 A 2 < . 80M c

� S 9,/�* . :,8H=,A 1 +�5 . 80=6< 2 < . 8HM . Ca. 1 < F�AB;�<?A 1 1 AB+6M)M 9 . : E = *0/�A 80A E +6� / =�A 80= :0M / =W2 .@0/ 1 C . 1 ;�2 < ;�/ � = . ;�A < 8�M 9,< C 2 < 8,F . C =,A 2 A,c P ; . 8,F)2 90/�AB@,@ E < 5 A 2 < . 80M?2 90AB2�5 . : E =�*0// 8,h6< M < . 8,/ =�A 1 /�@0AB1 A E E / E 2 . M / 1 < A E A 8H=�M / 1 < A E 2 . @0AB1 A E E / E 5 . 8,h�/ 1 2 / 1 M f02 < ;�/ � = . ;�A < 8;�: E 2 < @ E / Ï / 1 M f�AB80=�@0AB5 ��/ 2�M b�< 2 5 9,/ 1 M c P 8,/ b E A 8,F�:0A FB/�M 9 . : E =�*0/4=6/ h6/ E . @0/ =�2 . A E �E . b�2 9,/$@,1 . F�1 A ;�;�/ 1�2 . / Ï @,1 / M MY* . 2 9�=,A 2 A(� . b AB80=a2 < ;�/�5 . 80M 2 1 A < 8,2 Mi< 8�A45 . 805 < M /Bf< 8,2 :,< 2 < h�/�;�A 8,8,/ 1 c

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Page 56: robertfrench.org*0/ 1 24365. 2 2(701 / 805 9 3 :,*,; < 2 / =2. 9,/?>4/ @0ab1; / 8,2 c d e / 5 2 1 < a e0d 8,f < 8,/ 8,fa 80= g.; @,:,2 143,5 8h5 < 8ji a 1 2 a e 7,:

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G . ;�@,:,2 AB2 < . 80A Ei. 1 < F�A ;�<YA 1 5 9,< 2 / 5 2 :,1 / M$A 1 /4b�/ E E � M :,< 2 / = C . 1(M . ;�/?A @,@ E < 5 A 2 < . 80M c�Q . b�/ h�/ 1 f@,1 . F�1 A ;�;�< 8,F?A K 8,/ � FB1 AB< 8,/ =Hf E . b�� < 862 / 1 5 . 808,/ 5 2 . 1 < F�AB;�<65 . ;�@,:,2 / 1i< MiA(2 / =6< . :0Mi2 ABM �?2 . = .*,+?90A 80=ic SY. M .BE h6/�2 9,< M�@,1 . * E / ;�A?5 . ;�@,< E / 1ib4ABM�< 8,2 1 . =6:05 / =a2 . AB:,2 . ;�A 2 /(2 9,/(@,1 . 5 / M M . C@ E AB5 < 8,FaA 80=�1 . :,2 < 8,F E . FB< 5�/ E / ;�/ 862 Mi< 8�A?2 b . � =6< ;�/ 80M < . 80A E A E 2 / 1 80A 2 / � M E A 8,2 . 1 < F�AB;�<0A 1 1 AB+�c3�< 805 /�2 9,/�@,1 . * E / ; .BC(. @,2 < ;�A E E +J1 . :,2 < 8,F�A 8 . 1 < F6A ;�<$AB1 1 A +�< M4@01 . *0A * E +lU(I�� 5 . ;�@ E / 2 /BfA 80=�2 9,/�5 . ;�@,< E / 1YM 9 . : E =a1 :,8�< 8a@ .�E +68 . ;�< A E 2 < ;�/Bf 2 9,/$1 / M : E 2 AB8,2 . 1 < F6A ;�<6AB1 1 A +?< MY:0M :0A E E +M :,* . @,2 < ;�A E c P @0AB1 2 < A E M .�E :,2 < . 8)2 . 2 9,< M�@01 . * E / ;�b(A�M�@,1 / M / 802 / =�< 8�2 9,/ C . 1 ; . C < 2 / 1 A 2 < h�/. @,2 < ;�< � A 2 < . 80M cJ3�< ;�: E A 2 / =JA 808,/ A E < 8,FJb4ABM?:0M / =�2 . M / E / 5 2 < h�/ E +�A @,@ E +�;�:,2 AB2 < . 80M42 . 2 9,/A 1 1 AB+�c S 9,< M�1 / M : E 2 / =l< 8WAl=,/ 5 1 / ABM /J< 8 K 80A E A 1 1 A + M < � /J*,+l; . 1 /J2 90A 8���_���< 8�M . ;�/A @,@ E < 5 AB2 < . 80M c

S 9,/(5 . ;�@,< E / 1 f 5 . ;�*,< 80/ =4b(< 2 9�< 2 / 1 AB2 < h6/ . @,2 < ;�< � A 2 < . 8if @01 . h6< =6/ MYA4h�< A * E /�/ 8,h6< 1 . 8,�;�/ 8,2 C . 1(=6/ h6/ E . @,< 80F?@,1 . F�1 A ;�M C . 1(AB8 . 1 < F�A ;�<YA 1 1 A +6c S 9,/?1 / M : E 2 A 802$A 1 1 A +,M�AB1 /4M 2 < E E 8 . 2. @,2 < ;�A E fH*,:,2aAB1 /�M :6ö�5 < / 8,2 C . 1?/ Ï @0/ 1 < ;�/ 862 A E @,:,1 @ . M / M c N / 2 2 / 1 . @,2 < ;�< � A 2 < . 8�;�/ 2 9 . =,M

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A 1 /�=6< M 5 :0M M / =?< 8�G�90A @,2 / 1��6cYÁW< 2 9a2 9,/ M /�< ;�@,1 . h�/ ;�/ 862 M02 . 2 9,/ . @02 < ;�< � A 2 < . 8?;�/ 2 9 . =Hf 2 9,/5 . ;�@,< E / =�A 1 1 A +�M 9 . : E =�A @,@,1 . AB5 9)2 9,/?L�:0A E < 2 +a2 9HA 245 A 8)*0/aAB5 9,< / h�/ =�*,+�90A 80=)1 . :,2 < 8,F0c

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Page 58: robertfrench.org*0/ 1 24365. 2 2(701 / 805 9 3 :,*,; < 2 / =2. 9,/?>4/ @0ab1; / 8,2 c d e / 5 2 1 < a e0d 8,f < 8,/ 8,fa 80= g.; @,:,2 143,5 8h5 < 8ji a 1 2 a e 7,:

eÅÝ ëåí Ý � â�ä ê�ïåîgf

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