8
OHO L RED@HFUIUHD
8.8. Ihthr Oeihghdn
Rh`h ujujdyh, arhdn-arhdn jednnudhghd olihdnhd `esljhi udtug jedyhthghd hdngh. Dhjud, `hihj rhdnghlhd slstej `lnlthi, jlshidyh ghiguihtar hthu gajputer, hdngh `ldyhthghd `hihj oedtug ga`e older. [eihld ltu, jhslf ohdyhg ga`e ihld yhdn `lnudhghd `hihj suhtu slstej `lnlthi udtug jedyhthghd hdngh serth furuc hichoet.
8.?. Pumuhd
8. Jednethful cudnsl rhdnghlhd `ega`er `hd edga`er. ?. Jhjpu jedyusud rhdnghlhd `ega`er `hd edga`er `ednhd oerohnhl gajoldhsldyh.
?
OHO LL PLDMHUHD RU[PHGH
?.8 _hdnghlhd @ega`er
_hdnghlhd `ega`er h`hihf rhdnghlhd ianlgh gajoldhsladhi yhdn oercudnsl jednuohf ga`e older jedmh`l sldyhi `lsgrlt (Hdadyjaus, d.`.). _hdnghlhd ldl `hpht `loedtug jednnudhghd nerohdn HD@ ( (
) `hd A_
) (Hdadyjaus ?, d.`.).
[eouhf `ega`er fhrus jejedufl syhrht perhdkhdnhd j ≠ ?d. Shrlhoei j h`hihf gajoldhsl geiuhrhd `hd d h`hihf mujihf olt jhsughd. Mh`l, `ega`er ;
`ednhd ; jhsughd hghd jejlilgl jhgsljhi ? : 6 geiuhrhd. Fhdyh shtu geiuhrhd yhdn `l-hssert (`lhgtlcghd ‐ `luohf ge dlihl 8 udtug gad`lsl ianlgh pasltlc Whktlve-flnfZ hthu ge dlihl 2 udtug gad`lsl ianlgh denhtlc Whktlve-iawZ) `hihj shtu whgtu (ade-fat edka`e` ) (^l`lhdta, ?288). [htu gajoldhsl jhsughd fhdyh `hpht jewhglil shtu gajoldhsl geiuhrhd (Hdadyjaus, d.`.).
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Phoei ?.8. Phoei Geoedhrhd @ega`er ? ta 0
;
@hrl thoei `l hths, `hpht `louht cudnsl geiuhrhd seohnhl oerlgut =
@hrl pershjhhd terseout, jhgh rhdnghlhd nerohdndyh `hpht `louht sepertl ph`h nhjohr oerlgut =
Nhjohr ?.8. _hdnghlhd @ega`er ? ta 0
(Hdadyjaus, d.`.).
[eihld `ega`er ? ta 0, ter`hpht puih `ega`er ; ta 6 yhdn jednuohf tlnh ouhf jhsughd ge `hihj 6 ouhf geiuhrhd.
Nhjohr ?.?. Phoei Geoedhrhd `hd @lhnrhj Oiag @ega`er ; ta 6
(Hdadyjaus ?, d.`.).
0
LK `ega`er `lhpilghslghd ph`h seved senjedt , pednadtrai ihjpu ihiu ildths, pednhihjhthd jejarl, seohnhl `ega`er jhtrlg, `hd seohnhldyh (Hdadyjaus, d.`.).
Nhjohr ?.;. @eshld _eh`-Adiy J ejary (_AJ)
(^l`lhdta, ?288)
?.? _hdnghlhd Edga`er
Edga`er h`hihf rhdnghlhd ianlgh gajoldhsladhi yhdn jejpudyhl slcht yhdn oergeohilghd `ednhd `ega`er, yhltu oercudnsl udtug jednga`eghd suhtu sldyhi `lsgrlt jedmh`l geiuhrhd ga`e older (Hdadyjaus, d.`.). d
Edga`er older jednga`eghd ldcarjhsl (`hth) `hrl jhsughd ? ge `hihj ga`e geiuhrhd d-olt. [hihf shtu jhsughd (`hd fhdyh shtu jhsughd) fhrus jejpudyhl dlihl 8 (ade-fat edka`ldn ). Geiuhrhd jerepresedthslghd olihdnhd older yhdn jednl`edtlclghsl jhsughd jhdh yhdn jejpudyhl dlihl 8 (^l`lhdta, ?288).
5
Phoei ?.?. Phoei Geoedhrhd Edga`er 6 ta ;
@hrl thoei `l hths, `hpht `louht cudnsl geiuhrhd seohnhl oerlgut =
@hrl pershjhhd terseout, jhgh rhdnghlhd nerohdndyh `hpht `louht sepertl ph`h nhjohr oerlgut =
Nhjohr ?.0. _hdnghlhd Edga`er 6 ta ;
(Hdadyjaus, d.`.).
3
Mh`l, rhdnghlhd edga`er jednurhdnl mujihf olt yhdn `lperiughd udtug jerepresedthslghd suhtu ldcarjhsl (`hth). _hdnghlhd ldl `lnudhghd udtug trhdsjlsl ldcarjhsl `hihj slstej `lnlthi ghredh jednurhdnl mujihf shiurhd trhdsjlsl hthu ruhdn pedyljphdhd (^l`lhdta, ?288).
Jejouht suhtu `ega`er `hd edga`er `hpht `lihgughd `ednhd `uh khrh, yhltu (8) jednnudhghd nerohdn-nerohdn `hshr yhdn `lsusud jejoedtug cudnsl `ega`er hthu edga`er, `hd (?) jednnudhghd LK `ega`er `hd edga`er yhdn ohdyhg ter`hpht `l phshrhd (Hdadyjaus, d.`.), sepertl >0I[06, >0I[850, >0I[8;6, >0I[855, `hd seohnhldyh. @ednhd jednnudhghd LK `ega`er yhdn teihf h`h `l phshrhd, sesearhdn `hpht jerhdkhdn `ega`er `ednhd mujihf olt `hd geiuhrhd yhdn `lldnldghd (\u`lhdtlgh, ?288).
>
OHO LLL JEPA@AIANL RE_KAOHHD
;.8 Hiht `hd Ohfhd
H`hpud hiht `hd ohfhd yhdn `lnudhghd `hihj perkaohhd rhdnghlhd `ega`er h`hihf =
Nhjohr ;.8.8. [ujoer tenhdnhd 5 Sait @K
Nhjohr ;.8.?. Ghoei Ghwht Pudnnhi
Nhjohr ;.8.;. Rrata Oahr`
6
Nhjohr ;.8.0. Ihjpu IE@
Nhjohr ;.8.5. LK >0I[8;6
[e`hdnghd hiht `hd ohfhd yhdn `lnudhghd udtug jejoedtug rhdnghlhd edga`er h`hihf =
Nhjohr ;.8.3. [ujoer tenhdnhd 5 Sait @K
Nhjohr ;.8.>. Ghoei Ghwht Pudnnhi
<
Nhjohr ;.8.6. Rrata Oahr`
Nhjohr ;.8.<. Ihjpu IE@
Nhjohr ;.8.82. LK >0I[ serles
;.? Ihdnghf Rerkaohhd
_hdnghlhd `ega`er 8. Jedyusud rhdnghlhd `ega`er 0-olt `ednhd jednnudhghd `uh `ega`er older ?-olt. ?. Jednhjhtl fhsli geiuhrhddyh, geju`lhd jednlsl thoei yhdn teihf `lse`lhghd ph`h iejohr germh. ;. Jedyusud rhdnghlhd `ega`er 82-olt (yhdn `lnudhghd fhdyh ; olt shmh) `ednhd jednnudhghd `ega`er older ;-olt, nerohdn DHD@ 6 jhsughd, `hd oeoerhph nerohdn DAP. [eteihfdyh, jednuihdnl ihnl ihdnghf (?).
82
_hdnghlhd edga`er 8. Jedyusud rhdnghlhd `ega`er 6 ta ;. ?. Jednhjhtl fhsli geiuhrhddyh, geju`lhd jednlsl thoei yhdn teihf `lse`lhghd ph`h iejohr germh.
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OHO LS FH[LI @HD REJOHFH[HD
[hihf shtu medls `hrl rhdnghlhd `ega`er h`hihf `ega`er ;x6, yhltu `ega`er yhdn jednhjoli ; ouhf ldput `hd jedneiuhrghd 6 ouhf autput . @lhnrhj oiag `hrl `ega`er ;x6 `ltudmugghd ph`h Nhjohr ?.?. Udtug jednethful khrh germh `ega`er `hihj jedermejhfghd ga`e older jedmh`l olihdnhd `esljhi, oerlgut `loerlghd shildhd `hrl thoei geoedhrhd rhdnghlhd `ega`er ;x6 yhdn `lhjoli `hrl Nhjohr ?.?. = LDRUP
AUPRUP
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Phoei 0.8. Phoei Geoedhrhd @ega`er ;x6
Jhgdh `hrl dlihl-dlihl yhdn terterh ph`h thoei `l hths h`hihf =
Mlgh V, \, `hd ] tl`hg hgtlc, jhgh mhiur C2 hgt lc.
Mlgh V `hd \ tl`hg hgtlc, se`hdnghd ] hgtlc, jhgh mh iur C8 hgtlc.
8?
Mlgh V `hd ] tl`hg hgtlc, se`hdnghd \ hgtlc, jhgh mh iur C? hgtlc.
Mlgh V tl`hg hgtlc, se`hdnghd \ `hd ] hgtlc, jhgh mh iur C; hgtlc.
Mlgh \`hd ] tl`hg hgtlc, se`hdnghd V hgtlc, jhgh mhiur C0 hgtlc.
Mlgh \ tl`hg hgtlc, se`hdnghd V `hd ] hgtlc, jhgh mh iur C5 hgtlc.
Mlgh ] tl`hg hgtlc, se`hdnghd V `hd \ hgtlc, jhgh mhiur C3 hgtlc.
Mlgh V, \, `hd ] hgtlc, jhgh mhiur C> hgtlc.
Jhgsu` `hrl geh`hhd ’hgtlc‚ `l sldl yhltu mhiur yhdn oershdnguthd jejlilgl dlihl ianlgh 8 (hktlve-flnf), se`hdnghd ’tl`hg hgtlc‚ h`hihf geohilghddyh, yhgdl jejlilgl dlihl ianlgh 2 (hktlve-iaw). [lcht `hrl rhdnghlhd `ega`er ldl `lturudghd `hrl sgejh pednadverslhd olihdnhd older ge olihdnhd `esljhi (seohnhljhdh cudnsldyh). Hdnnhp V, \, `hd ] seohnhl ga`e older ; `lnlt se`hdnghd ohrlshd autput seohnhl olihdnhd `esljhi yhdn ter`lrl `hrl hdngh 2->.
222 : 2 Þ ?? + 2 Þ ?8 + 2 Þ ?2 : 2 (C2 hgtlc) 228 : 2 Þ ?? + 2 Þ ?8 + 8 Þ ?2 : 8 (C8 hgtlc) 282 : 2 Þ ?? + 8 Þ ?8 + 2 Þ ?2 : ? (C? hgtlc) 288 : 2 Þ ?? + 8 Þ ?8 + 8 Þ ?2 : ; (C; hgtlc) 822 : 8 Þ ?? + 2 Þ ?8 + 2 Þ ?2 : 0 (C0 hgtlc) 828 : 8 Þ ?? + 2 Þ ?8 + 8 Þ ?2 : 5 (C5 hgtlc) 882 : 8 Þ ?? + 8 Þ ?8 + 2 Þ ?2 : 3 (C3 hgtlc) 888 : 8 Þ ?? + 8 Þ ?8 + 8 Þ ?2 : > (C> hgtlc) Fhi yhdn shjh oerihgu udtug `ega`er 0x83. Rh`h `ega`er terseout, `lnudhghd 0 mhiur ldput yhdn hghd jedneiuhrghd 83 mhiur autput . Per`hpht se`lglt peroe`hhd ph`h autput yhdn `lfhslighd aief `ega`er 0x82. @ega`er ldl tl`hg hghd jedneiuhrghd autput hphpud ph`h ldput older yhdn mlgh
8;
`l`ega`eghd ge olihdnhd `esljhi hghd jedmh`l hdngh 82, 88, 8?, 8;, 80, `hd 85, `lghredhghd mhiur autput yhdn terse`lh fhdyh shjphl ph`h hdngh <. LDRUP
AUPRUP
Get
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JHPL
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JHPL
Phoei 0.?. Phoei Geoedhrhd @ega`er 0x82
H`hpud medls `ega`er ihld yhdn serldn `lphghl `hihj gefl`uphd sefhrl-fhrl h`hihf `ega`er OK@ ta > senjedt (0x>). Rrldslp germh `hrl `ega`er OK@ ta > senjedt jejlilgl gegfusushd tersed`lrl `ljhdh gajoldhsl `hrl setlhp ldputdyh `hpht jednhgtlcghd oeoerhph ilde autput seghilnus, yhdn geju`lhd hghd jednfl`upghd ihjpu IE@ yhdn oersesuhlhd.
Nhjohr 0.8. >-[enjedt @l spihy
80
Phoei geoedhrhd serth slrgult `ega`er OK@ ta >-senjedt `lperilfhtghd sepertl `l ohwhf ldl =
Nhjohr 0.?. Phoei Geoedhrhd OK@ ta >-[enjedt
Nhjohr 0.;. [lrgult @ega`er OK@ ta >-[enjedt
(@aktradlks, ?22<)
85
Edga`er h`hihf geohilghd `hrl rhdnghlhd `ega`er, sefldnnh prldslp germhdyh pud oergeohilghd. Mlgh `ega`er fhdyh jednhgtlcghd shtu mhiur autput udtug setlhp gajoldhsl ldput , edga`er `hpht jednhgtlcghd ieolf `hrl shtu mhiur udtug setlhp ldput yhdn `l`hphtdyh. Oerlgut ldl `loerlghd thoei geoedhrhd serth rhdnghlhd slrgult `hrl edga`er `ekljhi ta OK@ (edga`er 82x0) =
Nhjohr 0.0. Phoei Geoedhrhd Edga`er 82x0
Nhjohr 0.5. [lrgult Edga`er 82x0
Dlihl-dlihl yhdn jednlsl thoei geoedhrhd `l hths sesuhl `ednhd ghl`hf pednadverslhd olihdnhd `esljhi ge olihdnhd older. [eohnhl kadtaf, > 82 olih
83
`ldyhthghd `hihj ga`e older hghd jedmh`l 2888 ?. Mlgh mhiur ldput L> hgtlc, jhgh edga`er hghd jednhgtlcghd mhiur H, O, `hd K, se`hdnghd @ tl`hg hgtlc.
>82 : 2888? Ldput
K
O
H
[gejh yhdn shjh oerihgu udtug medls ldput yhdn ihld. Rerfltudnhd `l ohwhf ldl hghd jedmeihsghddyh sekhrh `ethli.
282 : 2222? (H, O, K, `hd @ tl`hg hgtlc) 882 : 2228? (H hgtlc, se`hdnghd O, K, `hd @ tl`hg hgtlc) ?82 : 2282? (O hgtlc, se`hdnghd H, K, `hd @ tl`hg hgtlc) ;82 : 2288? (H `hd O hgtlc, se`hdnghd K `hd @ tl`hg hgtlc) 082 : 2822? (K hgtlc, se`hdnghd H, O, `hd @ tl`hg hgtlc) 582 : 2828? (H `hd K hgtlc, se`hdnghd O `hd @ tl`hg hgtlc) 382 : 2882? (O `hd K hgtlc, se`hdnghd H `hd @ tl`hg hgtlc) >82 : 2888? (H, O, `hd K hgtlc, se`hdnghd @ tl`hg hgtlc) 682 : 8222? (@ hgtlc,se`hdnghd H, O, `hd K tl`hg hgtlc) <82 : 8228? (H `hd @ hgtlc, se`hdnghd O `hd K tl`hg hgtlc)
8>
OHO S GE[LJRUIHD
8) _hdnghlhd `ega`er h`hihf rhdnghlhd yhdn jed`ega`eghd ga`e older jedmh`l sldyhi-sldyhi `lsgrlt (olihdnhd `esljhi), se`hdnghd edga`er oercudnsl seohilgdyh. ?) Rrldslp germh `ega`er h`hihf `ednhd jednhgtlcghd fhdyh shtu mhiur autput udtug setlhp gajoldhsl ldput (gekuhil udtug `ega`er OK@ ta >-senjedt ), se`hdnghd edga`er `hpht jednhgtlcghd oeoerhph mhiur autput udtug setlhp ldput yhdn `l`hphtghddyh. ;) Per`hpht oerjhkhj-jhkhj medls rhdnghlhd `ega`er `hd edga`er, `l hdthrhdyh `ega`er ?x0, `ega`er ;x6, `ega`er 0x82, `ega`er 0x>, edga`er 6x;, `hd edga`er 82x0. Dajldhi terseout jednlgutl ghl`hf perhdkhdnhd d
rhdnghlhd j ≠ ? , `ljhdh j h`hihf mujihf gajoldhsl geiuhrhd `hd d h`hihf mujihf olt ldput udtug rhdnghlhd `ega`er, se`hdnghd j h`hihf mujihf gajoldhsl ldput `hd d h`hihf mujihf olt autput udtug rhdnghlhd edga`er. 0) Dlihl-dlihl yhdn jednlsl thoei-thoei geoedhrhd rhdnghlhd edga`er `hd `ega`er `hpht `lphfhjl jeihiul sgejh pedermejhfhd olihdnhd `esljhi ge ga`e older hthu pedngaverslhd `hrl ga`e older ge olihdnhd `esljhi.
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@HCPH_ RU[PHGH
Hdadyjaus. (d.`.). _hdnghlhd Ianlgh Gajoldhsladhi `hd [equedslhi . @lhgses ph`h thdnnhi ? Davejoer ?28?, pugui 8;.0> ^LO, `hrl fttp=//h`lsupe.clies.war`press.kaj/?282/2>/ja`uiQ;Q QrhdngQgajoQsequedslhi.p`c. Hdadyjaus ?. (d.`.). @eka`er, Edka`er, Kajphrhtar . @lhgses ph`h thdnnhi ? Davejoer ?28?, pugui 8?.;5 ^LO, `hrl fttp=//iekturer.eeplslts.e`u/~prljh/eiegtradlgh%?2`lnlthi/eiegtradlghQ`lnlthi8/ohfhdQhmhr/Oho6 hQ@eka`%?2Edka`.p`c. @aktradlks, E`ukhtladhi Ruoilsfldn car @eslnd & Pekfdaiany. (?22<). 0588O OK@ ta >-senjedt `eka`er `rlver . @lhgses ph`h thdnnhi 8? Davejoer ?28?, pugui 26.52 ^LO, `hrl fttp=//www.`aktradlks.ka.ug/0588.ftj. ^l`lhdta, Ega @l`lg. (?288). _hdnghlhd Gajoldhsladhi . @lhgses ph`h thdnnhi ? Davejoer ?28?, pugui 8;.0< ^LO, `hrl fttp=//`l`lg.oian.ud`lp.hk.l`/clies/?28?/2?/P[G?25-Guilhf82_hdnghlhdGajoldhsladhi-v?.p`c. \u`lhdtlgh, H`ltyh _lzgl. (?288). Putarlhi Pegdlg @lnlthi = @eka`er > [enjed. @lhgses ph`h thdnnhi ? Davejoer ?28?, pugui 8?.;0 ^LO, `hrl fttp=//www.h`ltyhrlzgl.det/?288/2>/tutarlhi-tegdlg-`lnlthi-`eka`er->senjed/.
