the abacus: one of the oldest calculating devices

8
-|UQ/WMHQV 7+($%$&86±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³EDOODULWKPHWLF´7KHGHVFULEHGGHYLFHKDVRQHEHDGLQDQXS SHUGLYLVLRQDQGIRXUEHDGVLQDORZHUSDUW>@7KHGHVFULSWLRQRIWKLVDQFLHQW&KLQHVHDEDFXVDQGWKH NQRZQLQWHUFRXUVHEHWZHHQ(DVWDQG:HVWJLYHUHDVRQWREHOLHYHWKH&KLQHVHDEDFXVZDVVX JJHVWHGE\ WKH5RPDQ,QFUHDVLQJWUDGHUHODWLRQVGXULQJWKH+DQ'\QDVW\%&±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

Upload: duongxuyen

Post on 02-Feb-2017

217 views

Category:

Documents


0 download

TRANSCRIPT

-|UQ�/�WMHQV7+(��$%$&86�± 21(��2)��7+(��2/'(67��&$/&8/$7,21��'(9,&(66RPH�LQIRUPDWLRQ�RQ�KLVWRULFDO�IDFWV��V\VWHPV��VSHFLDO�FRQVWUXFWLRQV�DQG�FDOFXODWLRQ�H[DPSOHV�����+LVWRU\�RI�WKH�DEDFXV�LQ�EULHI�7KH�DEDFXV�ZDV�RQH�RI�WKH�HDUOLHVW��DQG�PRVW�HIIHFWLYH�FDOFXODWLQJ�GHYLFHV��,Q�WKH�KDQGV�RI�D�VNLOOHG�RS�HUDWRU�LW�ZDV�D�SRZHUIXO�DLG�WR�FRPSXWDWLRQ��,Q�VHYHUDO�PDWKHPDWLF�KLVWRULFDOO\�OLWHUDWXUH��>����������@�\RX�FDQ�ILQG�RXW�WKDW�WKH�GHILQLWH�RULJLQ�RI�WKH�DEDFXV�LV�REVFXUH��%XW�WKHUH�LV�VRPH�UHDVRQ�IRU�EHOLHYLQJ�WKDW�LWV�HDUOLHVW�IRUP�ZDV�D�UHFNRQLQJ�WDEOH�FRYHUHG�ZLWK�VDQG�RU�ILQH�GXVW��LQ�ZKLFK�ILJXUHV�ZHUH�GUDZQ�ZLWK�D�VW \�OXV��WR�EH�HUDVHG�ZLWK�WKH�ILQJHU�ZKHQ�QHFHVVDU\��7KLV�GHVFULSWLRQ�LV�WKH�PHDQLQJ�RI�WKH�*UHHN�ZRUG�DED[�GXVW��DQG�IURP�WKDW��LW�VHHPV�WKH�DEDFXV�PD\�KDYH�HW\PRORJLFDOO\�GHULYHG��$V�\RX�NQRZ�WRGD\�ZH�XVH�WKH�/DWLQ�ZRUG�DEDFXV��9DULRXV�IRUPV�RI�D�OLQH�DEDFXV ZHUH�LQ�FRPPRQ�XVH�LQ�(XURSH�XQWLO�WKH�RSHQLQJ�RI�WKH�VHYHQWHHQWK�FHQWXU\��$�WKLUG�IRUP�RI�DEDFXV�DSSHDUHG�LQ�FHUWDLQ�SDUWV�RI�WKH�ZRUOG��LQVWHDG�RI�OLQHV�WKH�WDEOH�KDG�PRYDEOH�FRXQWHUV�VOLG�LQJ�XS�DQG�GRZQ�JURRYHV��$OO�WKUHH�W\SHV�RI�DEDFXVHV�ZHUH�IRXQG�LQ�DQFLHQW�5RPH�� WKH�GXVW�DEDFXV��WKH�OLQH�DEDFXV��DQG�WKH�JURRYHG�DEDFXV��7KH�URZV�UHSUHVHQWHG�XQLWV��VXFK�DV�WHQV��KXQGUHGV��DQG WKH�TXDQWLW\�RI�FRXQWHUV�LQ�WKH�URZV�UHSUHVHQWHG�D�QXPEHU�

5HSURGXFWLRQ�RI�D�5RPDQ�DEDFXV7KH�DEDFXV�EHFDPH�UDSLGO\�LQGLVSHQVDEOH��PDLQO\�EHFDXVH�RI�LWV�VLPSOLFLW\�RI�XVH�LQ�VRFLHWLHV�ZKHUH�QXP�EHU�V\VWHPV�ZHUH�FRPSOH[�DQG�GLIILFXOW�IRU�UHFNRQLQJ��7KLV�ZDV�WKH�FDVH�ZLWK�5RPDQ�QXPHUDOV��WU\��IRU�H[DPSOH��GLYLGLQJ�&&&;;;;;;,,,�E\�;;;,,,�LQ�\RXU�KHDG��>LW�LV������� ��@��%\�WKH�HQG�RI�WKH�VL[WHHQWK�FHQWXU\��WKH�PRGHUQ�QXPEHU�V\VWHP�EDVHG�RQ�+LQGX�$UDELF�PDWKHPDWLFV�KDG�EHFRPH�ZLGHVSUHDG��7KHUH�LV�D�VL[WK�FHQWXU\�&KLQHVH�UHIHUHQFH�WR�DQ�DEDFXV�RQ�ZKLFK�FRXQWHUV�ZHUH�UROOHG�LQ�JURRYHV��,W�VHHPV�WR�EH�WKH�PXFK�HDUOLHVW�ZRUN�ZKLFK�VSHDNV�RI�³EDOO�DULWKPHWLF´��7KH�GHVFULEHG�GHYLFH�KDV�RQH�EHDG�LQ�DQ�XS�SHU�GLYLVLRQ�DQG�IRXU�EHDGV�LQ�D�ORZHU�SDUW�>�@��7KH�GHVFULSWLRQ�RI�WKLV�DQFLHQW�&KLQHVH�DEDFXV�DQG�WKH�NQRZQ�LQWHUFRXUVH�EHWZHHQ�(DVW�DQG�:HVW�JLYH�UHDVRQ�WR�EHOLHYH��WKH�&KLQHVH�DEDFXV�ZDV�VXJJHVWHG�E\�WKH�5RPDQ��,QFUHDVLQJ�WUDGH�UHODWLRQV�GXULQJ�WKH�+DQ�'\QDVW\�����%&�± ����$&�ZLWK�WKH�5RPDQ�(PSLUH�DUH�LQGLFDWRUV IRU�WKLV�DVVXPSWLRQ�>�@��7KH�HDUOLHVW�SULQWHG�&KLQHVH�GRFXPHQW��VKRZLQJ�DQ�DEDFXV�LV�IURP������DQG�KDV�OHG�PDQ\�KLVWRULDQV�WR�FRQFOXGH�WKDW�WKH�DEDFXV�GLG�QRW�EHFRPH�NQRZQ�LQ�&KLQD�XQWLO�WKH�HQG�RI�WKH�VL[WHHQWK�FHQWXU\��1HYHUWKHOHVV�LW�LV�QRW�VXUH�WKDW�WKH�5RPDQ�DEDFXV�ZDV�WKH�GLUHFW�DQFHVWRU�RI�WKH�IRUP�RI�DEDFXV��ZKLFK�LV�VWLOO�XVHG�LQ�(DVW�$VLD��&KLQD��.RUHD��-DSDQ���5HIHUULQJ�WR�&KLQHVH�DQG�-DSDQHVH�+LVWRULDQV�WKHUH�DUH�VRPH��LQGLFDWLRQV�WKDW�WKH�GHYHORSPHQW�RI�DQ�DEDFXV�RFFXUV�LQ�WKH�(DVW��,QGLD��&KLQD��DQG�LQ�WKH�:HVW�LQGHSHQGHQW�QHDUO\�DW�WKH�VDPH�WLPH�>�@� 8QIRUWXQDWHO\�DUH�WKH�UHVXOWV�RI�VWXG\LQJ�WKLV�OLWHUDWXUH�FRQIXVLQJ�7KH�SUHVHQW�&KLQHVH�EHDG�DEDFXV��ZKLFK�LV�FDOOHG�VXDQSDQ LQ�0DQGDULQ�DQG�VRRSDQ�LQ�WKH�VRXWKHUQ�GLD�OHFW��ZDV�D�ODWHU�GHYHORSPHQW��SUREDEO\�DSSHDULQJ�LQ�WKH�WZHOIWK�FHQWXU\��DQG�GLG�QRW�FRPH�LQWR�FRPPRQ�XVH�WLOO�WKH�IRXUWHHQWK�FHQWXU\��7KH�-DSDQHVH�DUH�VDLG�WR�KDYH�REWDLQHG�D�IRUP�RI�DEDFXV�IURP�&KLQD��WKURXJK�.RUHD��LQ�DERXW�WKH�VL[WHHQWK�FHQWXU\��7KH�.RUHDQ�ZRUG�IRU�DEDFXV�LV� WVFKX�SDQ DQG�WKH�-DSDQHVH�ZRUG�LV�VRUREDQ� %RWK�ZRUGV�DUH�SUREDEO\�UHQGHULQJV�RI�WKH�&KLQHVH�VXDQSDQ��,Q�VSLWH�RI�GLIIHUHQW�ODQ�JXDJHV��DW�OHDVW�WKH\�VRXQGV�DOPRVW�VLPLODU��,Q�-DSDQ�WKH�IRUP�DQG�RSHUDWLRQDO�PHWKRGV�RI�WKH�DEDFXV�KDYH�XQGHUJRQH�VRPH�LPSURYHPHQWV��/LNH�WKH�SUHVHQW�GD\�&KLQHVH�VXDQSDQ��WKH�VRUREDQ�ORQJ�WLPH�KDG�WZR�EHDGV�DERYH�WKH�EHDP�DQG�ILYH�EHORZ��%XW�WRZDUG�WKH�FORVH�RI�WKH���WK FHQWXU\�LW�ZDV�VLPSOLILHG�E\�UHGXFLQJ�WKH�WZR�EHDGV�DERYH�WKH�EHDP�WR�RQH��DQG�ILQDOO\��DURXQG������WR������LW�DFTXLUHG�LWV�SUHVHQW�VKDSH�E\�RPLWWLQJ�\HW�DQRWKHU�EHDG��UHGXFLQJ�WKRVH�EHORZ�WKH�EHDP�IURP�ILYH�WR�IRXU�>�@��7KXV�WKH�SU HVHQW�IRUP�RI�WKH�VRUREDQ�ORRNV�PRUH�HOHJDQW��LV�PXFK�VPDOOHU�DQG�VRPHWLPHV�LW�KDV�PRUH�FROXPQV��DV�PDQ\��DV�WKLUW\�RQH��%XW�WKRVH�ZLWK�IHZHU�FROXPQV�����RU�����DUH�PRVW�RIWHQ�XVHG��1HYHUWKHOHVV�WKHUH�LV�RQH�LQ�WHUHVWLQJ�TXHVWLRQ��� 5HYLVHG�HGLWLRQ�RI�DQ�DUWLFOH�ZKLFK�LV�SXEOLVKHG�LQ�WKH�SURFHHGLQJV�RI�WKH���WK�,QWHUQDWLRQDO�0HHWLQJ�RI�6OLGH�5XOH�&ROOHFWRUV��� ����6HSWHPEHU��������,0�������$PVWHUGDP��

-��/�WMHQV� $EDNXV�2QOLQH�0XVHXP�����85/��ZZZ�MRHUQOXHWMHQV�GH 6HLWH�����:K\�GRHV�WKH�PRGHUQ�-DSDQHVH�VRUREDQ�KDYH�RQO\���EHDGV�RQ�HDFK�URG��OLPLWHG�WR�GLVSOD\�WKH�QXPEHU��"�$QG�ZK\�GRHV�WKH�DFWXDO�&KLQHVH�VXDQSDQ�KDYH���EHDGV�RQ�HDFK�URG��ZKLFK�FDQ�GLV�SOD\�LQ�WRWDO�WKH�QXPEHU���"�:KDW�DUH�WKH�DGYDQWDJHV�DQG�GLVDGYDQWDJHV"

%XW�ZKHWKHU�D�&KLQHVH�RU�D�-DSDQHVH�YHUVLRQ��ZLWK�WKH�EHDG�RU�URG�DEDFXV�PDQ\�FHQWXULHV�ORQJ�FD OFXOD�WLRQV�FRXOG�EH�GRQH�PXFK�PRUH�TXLFNO\�WKDQ�RQ�SDSHU��7KLV�W\SLFDO�$VLDQ�VSHFLDOLW\�FRPH�WR�HQG�ZLWK�WKH�VSUHDGLQJ�RI�HOHFWURQLF�FDOFXODWRUV��%XW�D�ILQDO�UHDU�XS�DJDLQVW�WKH�QHZ�WHFKQRORJ\�ZDV�ZKHQ�WKH�DEDFXV�ZRQ�RYHU�WKH�HOHFWULF�FDOFXODWRU�LQ�DQ�H[FLWLQJ�FRQWHVW�DW������LQ�7RN\R�>�@����&RQVWUXFWLRQV�RI�GLIIHUHQW�NLQGV�RI�ZLGH�VSUHDG�DEDFXVHV$�FURVVZLVH�EDU�GLYLGHV�WKH�DEDFXV�LQWR�WZR�SDUWV��7KH�XSSHU�SDUW�LV�FDOOHG�³KHDYHQ´�DQG�FRQVLVWV�RI�ILYH�YDOXH�EHDGV��7KH�ORZHU�SDUW�LV�FDOOHG�³HDUWK´�DQG�FRQVLVWV�RI�RQH�YDOXH�EHDGV��7KH�]HUR�SRVLWLRQ�RI�DOO�DEDFXVHV�LV��LI WKH�XSSHU�EHDGV�DUH�PRYHG�XS�DQG�WKH�ORZHU�EHDGV�DUH�PRYHG�GRZQ��2QO\�LI�RQH�RU�PRUH�EHDGV�DUH�PRYHG�WRZDUG�WR�WKH�EHDP��WKDQ�WKH\�UHSUHVHQW�D�QXPEHU�,Q�SULQFLSOH�WKH�URGV�UHSUHVHQW��VWDUWLQJ�IURP�WKH�ULJKW�VLGH�DQG�FRQWLQXLQJ�WR�WKH�OHIW�VLGH��WKH�³RQHV´��WKH�³WHQV´��WKH�³KXQGUHGV´�HWF��7KH�XVHU�KDV�WR�GHFLGH�ZKLFK�URG�WKH�³RQHV´�VKRXOG�EH��,I�WKHUH�DUH�QXPEHUV�ZLWK�YDOXHV�OHVV�WKDQ�RQH��LW�LV�FRQYHQLHQW�WR�SXW�WKH�FRO�XPQ�ZLWK�³RQHV´�MXVW�LQ�WKH�PLGGOH�RI�WKH�DED�FXV��6R�QXPEHUV�FDQ�JURZ�WR�ERWK�VLGHV��%XW�LI�WKHUH�DUH�RQO\�QXPEHUV�ZLWK�YDOXHV�IURP�RQH�DQG�KLJKHU�\RX�FDQ�VWDUW�MXVW�DW�WKH�ULJKW�VLGH�RI�WKH�IUDPH�GHYHORSLQJ�WKH�FDOFXODWLRQ�LQ�GLUHFWLRQ�RI�WKH�OHIW�VLGH�

&KLQHVH�VXDQSDQ�ZLWK�������EHDGV�RQ�HDFK�URG �

-DSDQHVH�VRUREDQ�ZLWK�������EHDGV�RQ�HDFK�URG �

-DSDQHVH�VRUREDQ�ZLWK�������EHDGV�RQ�HDFK�URG �,Q�DGGLWLRQ�WR�WKH�(DVW�$VLDQ�W\SHV�WKHUH�LV�D�WKLUG�IRUP��WKH�5XVVLDQ�DEDFXV�WKDW�LV�FDOOHG�VWVFKRW\��,W�LV�QRW�VXUH�ZKHWKHU�WKH�VWVFKRW\�LV�GHULYHG�IURP�WKH�VXDQSDQ��%XW�DQ\ZD\��GLUHFW�RU�LQGLUHFW��WKH�VWVFKRW\�KDV�EHHQ�LQ�5XVVLD�WKH�RQO\�FDOFXODWLRQ�GHYLFH�IRU�PDQ\�FHQWXULHV�XS�WR�QRZ��,W�LV�VXUSULVLQJ�WKDW�WKH�GLPHQVLRQV�RI�D�VWDQGDUG�RIILFH�VWVFKRW\�PHDVXUH�DERXW����FP�ZLGWK�E\����FP�KHLJKW��6PDOOHU�VWVFKRW\V��PDLQO\�IRU�VWXGHQWV�DUH�DOVR�LQ�XVH��7KH\�KDYH�D�VL]H�RI�DERXW����FP�ZLGWK�E\����FP�KHLJKW��7KH�PDLQ�GLIIHUHQFHV�WR�WKH�)DU�(DVW�DEDFXVHV�DUH�DV�IROORZV�x 7KH�LURQ�PDGH�URGV�DUH�O\LQJ�LQ�KRUL]RQWDO�SRVLWLRQ�DQG�WKH�EHDGV�KDYH�WR�PRYH�IURP�WKH�ULJKW�WR�WKH�OHIW�VLGH�RI�WKH�IUDPH�x 7KH�VWVFKRW\�GRHVQ¶W�KDYH�D�VHSDUDWHG�VHFWLRQ�IRU�PDNLQJ�JURXSV�RI�KLJKHU�YDOXHV��x 7KH�IUDPH�KDV����WR����URGV�ZLWK�HDFK����EHDGV��GH�SHQGV�RQ�WKH�VL]H�RI�WKH�VWVFKRW\���x 2QH�RU�WZR�URGV�DUH�HTXLSSHG�ZLWK�RQO\���EHDGV��7KLV�FROXPQV�DUH�IRU�FDOFXODWLRQV�ZLWK�IUDFWLRQV������5RXEOHV�RU�����.RSHNV��5XVVLDQ�VWVFKRW\

$V�\RX�VHH�WKH�VWUXFWXUH�LV�D�YHU\�VLPSOH�RQH��,Q�WKH�SLFWXUH�WKH�IRXUWK�URG��FRXQWHG�IURP�WKH�ERWWRP��UHSUHVHQWV�WKH�³RQHV´��7KH�QH[W�DERYH��VWDQGV�IRU�WKH�³WHQV´�DQG�VR�RQ��7KH�XSSHUPRVW�URG�UHSUHVHQWV�WKH�

-��/�WMHQV� $EDNXV�2QOLQH�0XVHXP�����85/��ZZZ�MRHUQOXHWMHQV�GH 6HLWH�����³PLOOLRQV´��2WKHUZLVH�WKH�URG�ZLWK�RQO\���EHDGV�KDV�DQRWKHU�IXQFWLRQ�WRR��LW�LQGLFDWHV�WKH�SRVLWLRQ�RI�WKH�FRPPD�DQG�WKH�QH[W�URG�MXVW�EHORZ�UHSUHVHQWV�WKH�³WHQWKV´�DQG�WKH�QH[W�EHORZ�LV�IRU�WKH�³KXQGUHGWKV´��5H�IHUULQJ�WR�0HQQLQJHU�>�@�WKH�IRUP�RI�WKH�5XVVLDQ�DEDFXV�VSUHDG�RXW�WR�)UDQFH�LQ������DQG�FRPHV�ODWHU�LQWR�FRPPRQ�LQ�*HUPDQ\�DV�D�W\SH�RI�FKLOGUHQ¶V�FDOFXODWRU�ZLWK����EHDGV�HDFK�RQ����URGV��8S�WR�QRZ�LW�LV�VWLOO�LQ�XVH�IRU�WHDFKLQJ�HOHPHQWDU\�PDWKHPDWLF�± DQG�LQ�RWKHU�SODFHV�RI�WKH�ZRUOG�WRR��HVSHFLDOO\�DV�D�³1XPEHU�$LG´�RU�³%DOO�$EDFXV´�LQ�WKH�86$����&DOFXODWLRQ�ZLWK�VXDQSDQ�DQG�VRUREDQ��$GGLWLRQ��������&KLQHVH�V\VWHP -DSDQHVH�V\VWHPSODFLQJ����PRYH�XS WKH�IRXU�ORZHU�EHDGV�LQ�WKH�ILUVW�FROXPQ��0RYH�GRZQ RQH�XSSHU�EHDG�LQ�WKH�VHFRQG�FROXPQ��7KH�SR�VLWLRQ�VKRZV���

SODFLQJ����PRYH�XS WKH�IRXU�ORZHU�EHDGV�LQ�WKH�ILUVW�FROXPQ��0RYH�GRZQ WKH�XSSHU�EHDG�LQ�WKH�VHFRQG�FRO�XPQ��7KH�SRVLWLRQ�VKRZV���DGGLQJ����0RYH�GRZQ RQH�XSSHU�EHDG�LQ�WKH�ILUVW�FROXPQ�DQG�PRYH�XS RQH�ORZHU�EHDG�LQ�WKH�ILUVW�FROXPQ��0RYH�XSIRXU�ORZHU�EHDGV�LQ�WKH�VHFRQG�FRO�XPQ��7KH�SRVLWLRQV�RI�DOO�EHDGV�WR�JHWKHU�GLVSOD\�WKH�UHVXOW�����

DGGLQJ�������FDQ�EH�DGGHG�EXW�QRW�WKH����%HFDXVH�RI�WR�OHVV�EHDGV�XVH�WKH�VXSSOHPHQWDU\�QXPEHU��������%XW�LQ�WKH�VHFRQG�FROXPQ�FDQQRW�EH�DGGHG����GLUHFWO\�UHGXQGDQW�EHDG�SRVLWLRQV�QHHG�FOHDULQJ�FDQFHO WKH�WZR�XSSHU���EHDGV�RI�WKH�ILUVW�DQG�VHFRQG�FROXPQ�DQG�PRYH�GRZQ�DOO�ORZHU�EHDGV�IURP�WKH�ILUVW�DQG�VHFRQG�FROXPQ��0RYH�XS RQH�ORZHU�EHDG�IURP�WKH�WKLUG�FROXPQ��ZKLFK�UHSUHVHQWV�WKH�UHVXOW�����ZLWK�RQO\�RQH�EHDG�

DGGLQJ����FDQFHO WKH�XSSHU�EHDG�LQ�WKH�VHFRQG�FROXPQ�DQG�PRYH�XSRQH�EHDG�LQ�WKH�WKLUG�FROXPQ��³KXQGUHGV´��7KH�UHVXOW�LV�QRZ����VXEWUDFW���DIWHU�PRYLQJ�GRZQ WKH�IRXU�EHDGV�LQ�WKH�³RQHV´�FROXPQ�WKH�ILQDO�UHVXOW�LV����

$�VNLOOHG�XVHU�RI�WKH�VXDQSDQ�LV�DEOH�WR�PDNH�WKH�VWHS�DIHU�DGGLQJ����GLUHFWOL\�WR�WKH�³RQH�KXQGUHG�EHDG´�DW�WKH�WKLUG�URG��%XW�LI�RQH�LVQ¶W�VR�IDPLOLDU�ZLWK�WKH�VSHHG\�SURFHGXUH��KH�FDQ�ZRUN�VWHS�E\�VWHS�ZLWK�WKH�VXDQSDQ��7KH�IROORZLQJ�SLFWXUHV�PDNH�LW�YLVLEOH�WKDW�DIWHU�DGGLQJ����WKUHH�PRUH�LQWHUPHGLDWH�VWHSV�KDYH�WR�EH�H[HFXWHG� DIWHU�DGGLQJ������VW�VWHS�RI�FOHDULQJ�FDQFHO DOO�ILYH�ORZHU�EHDGV�DQG�PRYH�GRZQWKH�VHFRQG�³��EHDG´��7KH\�WRJHWKHU�UHSUH�VHQW�DOVR�WKH�UHVXOW�����

�QG�VWHS�RI�FOHDULQJ�FDQFHO WKH�WZR�XSSHU���EHDGV�DQG�PRYH�XSRQH�ORZHU�EHDG�IURP�WKH�VHFRQG�FROXPQ��ZKLFK�UHSUHVHQWV�WKH�³WHQV´��7KH�UH�VXOW�LV�VWLOO�����

�UG�VWHS�RI�FOHDULQJ�FDQFHO DOO�ILYH�ORZHU�EHDGV�RI�WKH�VHFRQG�FRO�XPQ�DQG�PRYH�GRZQ WKH�VHF�RQG�³��EHDG´�

-��/�WMHQV� $EDNXV�2QOLQH�0XVHXP�����85/��ZZZ�MRHUQOXHWMHQV�GH 6HLWH�����7KLV�H[DPSOH�VKRZV�WKDW�WKH�&KLQHVH�VXDQSDQ�ZLWK�������EHDGV�FDQ�GLVSOD\�WKH�VDPH�QXPEHU�LQ�GL IIHUHQW�ZD\V��%XW�VNLOOHG�XVHUV�GRQ¶W�SHUIRUP�FDOFXODWLRQV�LQ�WKLV�PDQQHU�OLNH�GHPRQVWUDWHG�KHUH��7KH�PHWKRG�RI�WKLQNLQJ�E\�RSHUDWLQJ�DQ�DEDFXV�LV�LPSRUWDQW��7KH�XVHU�QRUPDOO\�LV�WKLQNLQJ�RI�WKH�QH[W�KLJKHU�SRZHU�WR�WHQ��H�J����DUH������RU����DUH������RU����LV�������DQG�VR�RQ��0HQWDO�FDOFXODWLRQ�LV�GLIIHUHQW�IURP�SHQFLO�DULWKPH�WLF��ZKLFK�LV�SHUIRUPHG�LQ�WKLQNLQJ�RI�WKH�WRWDO��$EDFXV�XVHUV¶�PHQWDO�FDOFXODWLRQV�DUH�OLPLWHG�WR�D�PD[LPXP�RI�WHQ�DQG�HDFK�VWHS�LV�SHUIRUPHG�LQGHSHQGHQWO\�ZLWKRXW�EHLQJ�FRQFHUQHG�ZLWK�WKH�WRWDO��2Q�WKH�RQH�KDQG��LQ�FDVH�RI�WKH�-DSDQHVH�VRUREDQ�LV�WR�FRQVLGHU�WKDW�EHFDXVH�RI�WKH�UHGXFHG�QXPEHU�RI�EHDGV�WKLV�PHQ�WLRQHG�SULQFLSOH�RI�PHQWDO�FDOFXODWLRQ�LV�PXFK�PRUH�LPSRUWDQW�WKDQ�IRU�WKH�&KLQHVH�VXDQSDQ��2Q�WKH�RWKHU�KDQG�WKH�&KLQHVH�VXDQSDQ�ZLWK�WZR�ILYH�YDOXH�EHDGV�JLYHV�DGYDQWDJH�IRU�GLYLVLRQ�FDOFXODWLQJ�WR�LQGLFDWH�LQ�RQH�FROXPQ�D�KLJKHU�QXPEHU�RI�������6SHFLDO�DEDFXVHV������³/HH¶V��,PSURYHG��$EDFXV´ LQYHQWHG�DURXQG������E\�/HH�.DL�&KHQ��7DLZDQ��>�@

³$X[LOLDU\�2SHUDWLRQ�)LHOGV´OHIW�$�2�ILHOG�ZLWK���������������������ULJKW�$�2�ILHOG�ZLWKJUHHQ�FRORXUHG�EHDGV��������������ZKLWH�FRORXUHG�EHDGV�XSSHU�GHFN�³$X[LOLDU\�2SHUDWLRQ�)LHOGV´$�2�ILHOGV

SODFH�VHWWLQJ�YHUQLHU

ORZHU�GHFN�³3ULQFLSOH�2SHUDWLRQ�)LOHG´3�2�ILHOG

PRYDEOH�LQGLFDWRU7KLV�GRXEOH�DEDFXV�KDV�D�VL]H�RI���FP�E\���FP��,W�FRPELQHV�D�WUDGLWLRQDO�&KLQHVH�VXDQSDQ�������ZLWK�D�-DSDQHVH�VRUREDQ��������7KH�ORZHU�SDUW�RI�WKH�VXDQSDQ�ZLWK�WKH�ELJ�EHDGV�LV�WKH�PDLQ�DEDFXV��7KLV�VHF�WLRQ�LV�FDOOHG�³3ULQFLSOH�2SHUDWLRQ�)LOHG´�3�2��7KH�XSSHU�DEDFXV�FRQWDLQLQJ�VPDOO�EHDGV�LV�DQ�DX[LOLDU\�DEDFXV��7KLV�VHFWLRQ�LV�VSOLW�LQ�D�OHIW�DQG�ULJKW�SDUW�± LW�LV�FDOOHG�³$X[LOLDU\�2SHUDWLRQ�)LHOGV´��OHIW�$�2�DQG�ULJKW�$�2���/HH�.DL�&KHQ�SUDLVHV�DV�DQ�LPSRUWDQW�PHULW�RI�KLV�LP�SURYHG�DEDFXV�WKH�FRPEL�QDWLRQ�DV�ZHOO�DV�WKH�SDUWL�WLRQ�RI�WKH�WKUHH�FRXQWHUV��3ODFLQJ�GLIIHUHQW�FDOFXOD�WLRQV�PDNHV�PRUH�FRPSOH[�SURFHVVHV�YLVLEOH�FRPSDUD�EOH�WR�DQ�ROG�VW\OH�DEDFXV�

&RQVWUXFWLRQ�GHWDLO�3ODFH�VHWWLQJ�YHUQLHU��D�ZKLWH�PRYDEOH�UXEEHU�VWULQJ�ZLWK�UHG�GRW�PDUN�HUV�PDNHV�LW�HDVLHU�WR�IL[�WKH�SRVLWLRQV�IRU�WKH�³RQHV´��³WHQV´��³KXQGUHGV´�DQG VR�RQ�

-��/�WMHQV� $EDNXV�2QOLQH�0XVHXP�����85/��ZZZ�MRHUQOXHWMHQV�GH 6HLWH������������([WUDFWLRQ�RI�VTXDUH�URRWV�ZLWK�WKH�/HH¶V�DEDFXV�$W�ILUVW��UHPHPEHU��WKH�PHWKRG�RI�H[WUDFWLQJ�VTXDUH�URRWV�ZH�OHDUQHG�LQ�VFKRRO�LV�EDVHG�RQ�WKH�WHUP�DV�WKH�ELQRPLQDO�IRUPXOD��D�E�� �D� ���DE���E���$IWHU�VHWWLQJ��WKH�H[WUDFWLRQ�LV�D�SURFHVV�E\�PDNLQJ�GLYLVLRQV�

BBBB¥���� � UHVXOW�����������������BBBB������������������BBBB�:LWK�WKH�DLG�RI�DQ�DEDFXV�WKH�H[WUDFWLRQ�PHWKRG�LV�WXUQHG�LQWR�D�SURFHVV�RI�DGGLWLRQV�DQG�VXEWUD FWLRQV��7KLV�PHWKRG�ORRNV�YHU\ HDV\�WR�KDQGOH��EXW�LW�LV�VRPHZKDW�VORZ�DQG�WHGLRXV��(VSHFLDOO\�LQ�FDVH�RI�ORQJ�VTXDUH�URRW�QXPEHUV�D�VHULHV�RI�DGGLWLRQV�DQG�VXEWUDFWLRQV�ZLOO�WDNH�SODFH�SUHSD�UDWLRQ� 3ODFH�WKH�QXPEHU�����IURP�ZKLFK�WKH�VTXDUH�URRW�LV�WR�EH�H[WUDFWHG�LQ�WKH�FHQWUH�RI�WKH�3�2�ILHOG��'LYLGH�WKH�VTXDUH�QXPEHU�LQWR�WZR�JURXSV��WKH�ILUVW�JURXS�FRQWDLQLQJ�RQH�ILJXUH����DQG�WKH�RWKHU�JURXS�FRQWDLQLQJ�WZR�ILJXUHV����DQG����

0RYH�WKH�LQGLFDWRU�WR�PDUN�RXW�WKH�ILUVW�JURXSVWHS�� 3ODFH���RQ�WKH�ILUVW�FROXPQ�RI�WKH�ULJKW�$�2�ILHOG��7KLV�LV�QRZ�WKH�³URRW´�QXPEHU��6XEWUDFW���IURP�WKH�ILJXUH�RI�WKH�ILUVW�³VTXDUH´�JURXS�LQ�WKH�3�2�ILHOG��QDPHO\����OHDYLQJ���

VWHS�� $GG���WR�WKH�URRW�QXPEHU���PDNLQJ���DQG�VXEWUDFW�WKH�VXP���IURP�WKH�ILUVW�JURXS�LQ�WKH�3�2�ILHOG��7KHUH�LV�QRZ���

VWHS�� $GG���WR�WKH���LQ�WKH�³URRW´�QXPEHU�LQ�WKH�$�2�ILHOG��1RZ�WKHUH�DUH�WZR�FROXPQV�WR�EH�FRQVLGHU��7R�WKH�YDOXH�RI����DGG�����7KH�VXP�RI�WKH�QHZ�³URRW´�QXPEHU�LV����

0RYH�WKH�LQGLFDWRU�LQ�WKH�3�2�ILHOG�WZR�FROXPQV�WR�WKH�ULJKW��,Q�WKH�VTXDUH�QXPEHU�DUH�QRZ�����

-��/�WMHQV� $EDNXV�2QOLQH�0XVHXP�����85/��ZZZ�MRHUQOXHWMHQV�GH 6HLWH�����7R�DYRLG�D�ERULQJ�UHSHWLWLRQ�RI�SLFWXUHV�ZLWK�FHUWDLQ�QXPEHU�FRQVWHOODWLRQV��DOO����VWHSV�DUH�VKRZQ�LQ�WKH�IROORZLQJ�WDEOH��>�@

³���´�RSHUDWLRQV�RQ�WKH�OHIW�$�2�ILHOG ³�� ³�RSHUDWLRQV�RQ�WKH�3�2�ILHOG6WHS �VW�GLJLW �QG�GLJLW ILUVW�JURXS VHFRQG�JURXS� � �� � �� � � � �� � � �� � � �� � � �� � � �� � � �� � � ��� � � ��� � � �� � � � ��� ������� ���������� ���+HUH�DUH�WKH�ODVW�ILQDO�VWHSV��1R�������DQG�����DW�WKH�DEDFXV�VWHS��

$GG���WR�WKH�URRW�QXPEHU����PDN�LQJ����DQG�VXEWUDFW�WKH�VXP����IURP�WKH�VTXDUH�QXPEHU�LQ�WKH�3�2�ILHOG��OHDYLQJ����

VWHS���

$GG���WR�WKH�URRW�QXPEHU����PDNLQJ����DQG�VXEWUDFW�WKH�VXP����IURP�WKH�VTXDUH�QXPEHU�LQ�WKH�3�2�ILHOG��OHDYLQJ�]HUR�

VWHS���

$GG���WR�WKH�³URRW´�QXPEHU��PDNLQJ�����'LYLGH����E\����WKH�TXRWLHQW����WKXV�REWDLQHG�LV�WKH�VTXDUH�URRW�UHTXLUHG�$V�ZH�VHH��WKH�SURFHGXUH�LV�QRW�PRUH�WKDQ�DGGLQJ�D�QXPEHU�WR�WKH�³URRW´�QXPEHU�DQG�VXEWUDFWLQJ�WKH�VXP�IURP�WKH�³VTXDUH´�QXPEHU�XQWLO�WKH�RULJLQ�QXPEHU�LV�H[KDXVWHG������$Q�DEDFXV�ZLWK�GRXEOH�ILYH�EHDGV�RQ�HDFK�URG�8VDEOH�IRU�D�TXLQDU\�QXPHULFDO�V\VWHP"�0RUH�TXHVWLRQV�WKDQ�DQVZHUV�

7KLV�DEDFXV�IURP�9LHWQDP�KDV�LQ�WKH�ORZHU�DQG�LQ�WKH�XSSHU�VHFWLRQ�HDFK���EHDGV�RQ�HDFK�URG��,W�PHDVXUHV�����PP�E\����PP��

-��/�WMHQV� $EDNXV�2QOLQH�0XVHXP�����85/��ZZZ�MRHUQOXHWMHQV�GH 6HLWH�����:KDW�NLQG�RI�FRQFHSW�RU�FDOFXODWLRQ�V\VWHP�LV�EHKLQG�WKLV�XQXVXDO�SODFHPHQW�RI�EHDGV")LUVW�VXSSRVLWLRQ��7KH����EHDGV�LQ�WRWDO�RQ�HDFK�URG�LQGLFDWH��WKDW�WKLV�DEDFXV� LV�XVDEOH�LQ�WKH�VDPH�ZD\�OLNH�WKH�5XVVLDQ�VWVFKRW\��EDVHG�RQ�WKH�GHFLPDO�V\VWHP��)URP�WKH�ULJKW�WR�WKH�OHIW�UHSUHVHQWV�HDFK�FROXPQ�D�SRZHU�WR�����,I�VR��WKDQ�WKH�KRUL]RQWDO�EHDP��VHSDUDWLQJ�WKH�DEDFXV�LQWR�WZR�VHFWLRQV��KDV�QR�VSHFLDO�IXQFWLRQ�6HFRQG�VXSSRVLWLRQ��LI�WKH�XSSHU�ILHOG�LV�QRW�LQ�XVH��,I�ZH�VZLWFK�WR�D�TXLQDU\�V\VWHP��EDVH�����WKDQ�WKH�ILUVW�URG�UHSUHVHQWV�WKH�³RQHV´����7KH�QH[W�URG�VWDQGV�IRU�WKH�³ILIWK´�����WKDQ�IROORZ�WKH�³WZHQW\�ILIWK´�����WKH�³KXQGUHGWZHQW\�ILIWK´������DQG�VR�RQ�IROORZLQJ�E\�WKH�RWKHU�SRZHUV�WR����2Q�HDFK�URG�ZH�FDQ�FRXQW����EHDGV�ZLWK�WKH�VDPH�YDOXH�RI�� [��%XW�LQ�SULQFLSOH�DOO�EHDGV��FRXQWLQJ�IURP���WR�����LQ�WKH�XSSHU�VHFWLRQ�DUH�UHGXQGDQW�EHFDXVH�WKH�VDPH�QXP�EHU�FDQ�GLVSOD\HG�E\�WUDQVIRUPDWLRQ�WR�WKH�URG�QH[W�OHIW��7KH�FROXPQ�KDV�WR�EH�FOHDUHG��WKLV�LV�WKH�VDPH�SURFHGXUH�OLNH�WKH�VXDQSDQ�ZLWK�����EHDGV���,Q�WKLV�FDVH�WKH�KRUL]RQWDO�EHDP�KDV�QR�VSHFLDO�IXQFWLRQ�WRR�DQG�WKH�XSSHU�ILYH�EHDGV�RQ�HDFK�URG�DUH�XQQHFHVVDU\�7KLUG�VXSSRVLWLRQ�:LWK�LQWHJUDWLRQ�RI�WKH�XSSHU�ILHOG�LW�PD\�EH�XVDEOH�IRU�D�FRPELQDWLRQ�RI�GHFLPDO�DQG�TXLQDU\�V\VWHP�

������GLVSOD\HG�LQ�D� TXLQDU\�V\VWHPWKH�XSSHU�ILHOG�LV�QRW�LQ�XVHRQO\�EHDGV�RI�WKH�ORZHU�ILOHG�DUH�QHF�HVVDU\�WR�GLVSOD\�QXPEHUV�LQ�D�TXLQDU\�V\VWHP

�� �� �� �� �� ��

7UDQVIRUPDWLRQ�IURP�WKH�TXLQDU\�WR�WKH�GHFLPDO�V\VWHP�� � � � �� �� �

� �� ��� �� ��

� �� ���� �� ���GHFLPDO� ���

%XW�WKH�EDVLF TXHVWLRQ�UHPDLQV��,V�LW�SRVVLEOH�WKDW�WKLV�DEDFXV�IURP�9LHWQDP�LV�XVHG�IRU�D�TXLQDU\�V\VWHP"�2Q�WKH�RWKHU�KDQG��$�&KLQHVH�VXDQSDQ�VKRZV�WKH�VDPH�FKDUDFWHULVWLF�LI�ZH�IRFXV�RQ�WKH�ORZHU�VH FWLRQ�ZLWK���EHDGV�RQO\��:KDW�SXUSRVH�GR�WKH�XSSHU���EHDGV�KDYH"�7KH LGHD�RI�D�TXLQDU\�V\VWHP�LV�WHPSWLQJ�RI�FRXUVH�EXW�PD\�EH�DEVROXWHO\�ZURQJ��5HFHQWO\�,�IRXQG�D�ZHE�VLWH�IURP�D�0DOD\VLDQ�DEDFXV�PXVHXP�ZLWK�D�ORW�RI�DEDFXV�SLFWXUHV��7ZR�RI�WKHP�DUH�DOVR�HTXLSSHG�ZLWK�������EHDGV��8QIRUWXQDWHO\�ZDV�WKHUH�QR�LQIRUPDWLRQ�DYDLODEOH��>�@�,�WU\�WR�IROORZ�DQRWKHU�LGHD��D�SRVVLEO\�FRUUHODWLRQ�EHWZHHQ�ILQJHU�FRXQWLQJ�DQG�XVH�RI�DQ�DEDFXV��2I�FRXUVH�FRXQWLQJ�V\VWHPV�DQG�FDOFXODWLRQ�V\VWHPV�DUH�QRW�WKH�VDPH��,Q�OLWHUDWXUH�,�IRXQG�D�UHIHUHQFH�RI�XVLQJ�WKH�UDUH�EDVH���V\VWHP��*HRUJHV�,IUDK�PHQWLRQHG�WKDW�LQ�WKH�%RPED\�UHJLRQ�RI�,QGLD�VRPH�PHUFKDQWV�VWLOO�XVH�WRGD\�DQ�LQWHUHVWLQJ�FRXQWLQJ�WHFKQLTXH�ZLWK�ILQJHUV�>�@��,Q�DGGLWLRQ��,�ZDV�ZLWQHVV�RI�XVLQJ�DQRWKHU�ILYH�QXPHULFDO�V\VWHP�E\�ILQJHUV�LQ�6RXWK�.RUHD��+HUH�VRPH�EDVLF�LQIRUPDWLRQ�������8VLQJ�ILQJHUV��WKH�QDWXUDO�EDVH�IRU�D�TXLQDU\�V\VWHP7RGD\�WKHUH�DUH�YHU\�IHZ�TXLQDU\�V\VWHPV�H[LVWLQJ�LQ�D�SXUH�VWDWH��,Q�6RXWK�.RUHD¶V�KDUERXU�FLW\�3XVDQ�,�DWWHQGHG������DW�D�ILVK�DXFWLRQ�DQG�GHWHFWHG�ELGGHUV�XVLQJ�D�RQH�KDQG�TXLQDU\�V\V WHP�ZLWKRXW�VKRXWLQJ�WKHLU�ELGV��DV�QRUPDOO\�KDSSHQHG�DW�DXFWLRQV��

-��/�WMHQV� $EDNXV�2QOLQH�0XVHXP�����85/��ZZZ�MRHUQOXHWMHQV�GH 6HLWH�����

:DOO�SRVWHU�ZLWK�LQVWUXFWLRQV�LQ�WKH�DXFWLRQ�KDOO .RUHDQ�ELGGHU�DW�D�ILVK�DXFWLRQ��/RRN�DW�WKH�MDFNHWV�±WKH\�DUH�XVHG�DV�VKLHOG�DJDLQVW�FRQFXUUHQWV�,W�LV�QRW�FOHDU�WKDW�WKHUH�LV�D�FORVH�UHODWLRQVKLS�EHWZHHQ�D�TXLQDU\�QXPHULFDO�V\VWHP��ZHDWKHU�DSSOLHG�E\�RUDO�QXPEHUV�RU�VKRZQ�E\�ILQJHUV��DQG�WKH�DEDFXV�ZLWK�������EHDGV�DV�VKRZQ�DERYH��%XW�LW�LV�WKLQNDEOH�����&RQFOXVLRQ7KHUH�LV�QR�GRXEW��6LQFH�DERXW����\HDUV�WKH�DEDFXV�KDV�ORVW�KLV�LPSRUWDQFH�DV�D�FDOFXODWLRQ�GHYLFH�IRU�PDQ\�FHQWXULHV��,Q�WKH�YLHZ�RI�PRVW�RI�WKH�SHRSOH�WRGD\��DQ�DEDFXV�LV�QRW�PRUH�WKDQ�D�QLFH�DFFHVVRU\�RI�W\SLFDO�&KLQHVH��.RUHDQ�RU�-DSDQHVH�FXOWXUH��$QG�EHFDXVH�RI�LWV�YHU\�VLPSOH�FRQVWUXFWLRQ�VRPH�SHRSOH�WKLQN�WKDW�LW�LV�QRW�ZRUWKZKLOH�WR�ORRN�EHKLQG�WKH�LGHD�RI�PHQWDO�DULWKPHWLF�DQG�SULPLWLYH�H[HFXWLRQ�E\�PRY�LQJ�EHDGV��6LPSOH�WKLQJV�DUH�DOZD\V�IDVFLQDWLQJ��HVSHFLDOO\�LI�ZH�FRQVLGHU�WKDW�$VLDQ�SHRSOH�KDQGOH�DQ�DEDFXV�ZLWK�H[FHOOHQW�PDVWHUVKLS��7KH�GHYHORSPHQW�RI GLIIHUHQW�W\SHV�RI�DEDFXVHV�DUH�SURRI�HQRXJK�����5HIHUHQFHV>�@�$EDFXV�0XVHXP�DW�WKH�0DOD\VLDQ�ZHE�VLWH�RI�$/2+$�0HQWDO�$ULWKPHWLFKWWS���ZZZ�DORKDPD�FRP�DEPXVHXP�IXQFWLRQDO�DEDFXV�LQGH[��KWPO �ZHE�OLQN�IURP�-XO\��QG �����>�@�*UR�HV�+DQGEXFK�GHU�0DWKHPDWLN��.|OQ�����>�@�+DUWPXWK��0D[LPLOLDQ� 9RP�$EDNXV�]XP�5HFKHQVFKLHEHU���1DFKGUXFN�GHU�$XVJDEH�YRQ��������2VQDEU�FN��2WWR�=HOOHU������>�@�,IUDK��*HRUJHV� )URP�RQH�WR�]HUR��(QJOLVK�WUDQVODWLRQ�RI�³+LVWRLUHXQLYHUVHOOH�GHV�FKLIIUHV´��+DUULVRQEXUJ�9LUJLQLD��������,6%1���������������>�@�.RMLPD��7DNDVKL� 7KH�-DSDQHVH�$EDFXV�± LWV�XVH�DQG�WKHRU\��5XWODQG��YHUPRQW��7RN\R�����>�@�.RMLPD��7DNDVKL� $GYDQFHG�DEDFXV��-DSDQHVH�WKHRU\�DQG�SUDFWLFH��5XWODQG��9HU�PRQW� 7RN\R�����>�@�/HH�.DL�&KHQ� $�5HYROXWLRQ�RI�&KLQHVH�&DOFXODWRUV��+RZ�WR�OHDUQ�/HH¶V�DEDFXV��'RZQORDG�RQ�WKH�ZHEVLWH�RI�/XLV�)HUQDQGHV�KWWS���ZZZ�HH�U\HUVRQ�FD��������(HOI�DEDFXV�OHHDEDFXV�LQGH[�KWPO�FXEHUW>�@�0HQQLQJHU��.DUO� .XOWXUJHVFKLFKWH�GHU�=DKOHQ��%UHVODX�����>�@�5RQDQ��&�$����1HHGKDP��-���7KH�VKRUWHU�VFLHQFH�DQG�FLYLOLVDWLRQ�LQ�&KLQD�,,��&DP�EULGJH�������BBBBBBBBBBBBBBBBBBBBBBBBBBB$OO�SKRWRV�PDGH�E\�¤¤ -��/�WMHQV