Lub keeb kwm ntawm cov zauv thiab tus naj npawb system, positional system (luv luv)

Lub keeb kwm ntawm cov zauv thiab tus xov tooj system yog zoo txuas, vim hais tias cov xov tooj system, thiab yog ib txoj kev teev xws paub daws teeb lub tswv yim zoo li tus xov tooj. Cov npe no tsis thov heev dua lwm yam rau hauv lub teb ntawm kev kawm txog zauv, vim hais tias tag nrho cov no yog ib feem tseem ceeb ntawm tib neeg lub kab lis kev cai raws li ib tug tag nrho. Vim hais tias thaum to taub lub keeb kwm ntawm tus xov tooj thiab tus xov tooj tshuab, luv luv nphav thaum ntau yam ntawm lub keeb kwm ntawm civilizations uas tsim lawv. Systems yog feem ntau muab faib mus rau hauv positional nonpositional thiab mixed. Los ntawm lawv cov alternation yog tag nrho zaj dab neeg ntawm tus xov tooj thiab tus xov tooj tshuab. Tig cev system - yog zoo li no hais tias tus nqi denoted los ntawm tus nab npawj nyob rau hauv cov ntaub ntawv tus xov tooj, nyob ntawm seb nws txoj hauj lwm. Nyob rau hauv nepozitsionnyh systems, ntsig txog, tsis muaj zoo li dependence. Noob neej tsim thiab mixed tshuab.

Txoj kev tshawb no ntawm tus xov tooj tshuab nyob rau hauv cov tsev kawm ntawv

Niaj hnub no zaj lus qhia "Keeb kwm ntawm tus xov tooj thiab tus xov tooj tshuab" yuav tsum muaj nyob rau hauv lub 9 qib kawm rau cov hoob kawm nyob rau hauv computer science. Tseem ceeb tshaj nws cov tswv yim muaj nuj nqis - mus kawm txhais tooj los ntawm ib tug xov tooj system mus rau lwm lub (tshwj xeeb tshaj yog los ntawm tus zauv rau binary). Txawm li cas los, lub keeb kwm ntawm tus xov tooj thiab tus xov tooj tshuab yog ib feem ntawm cov keeb kwm raws li ib tug tag nrho thiab nws yuav Nkij los txuam rau kuj yuav kawm txog lub tsev kawm ntawv cov ntaub ntawv kawm. Nws kuj tseem txhim kho hnub no advocated ib multidisciplinary mus kom ze. Raws li ib feem ntawm cov kev hom keeb kwm, nyob rau hauv tus, nws yuav tsum kawm tsis tau tsuas yog lub keeb kwm ntawm nyiaj txiag txoj kev loj hlob, kev sib raug zoo thiab kev nom kev tswv taw, cam thiab kev tsov kev rog, tab sis kuj mus rau ib tug me me raws li lub keeb kwm ntawm tus xov tooj thiab tus xov tooj tshuab. 9 nyob rau hauv lub chav kawm ntawm lub computer hauv chav kawm ntawv nyob rau hauv cov ntaub ntawv no yuav tsum nyob rau hauv cov nqe lus ntawm translation xov tooj los ntawm ib tug system mus rau lwm lub system muab ib tug loj npaum li cas naj npawb ntawm cov piv txwv ntawm cov yav tas los kawm ntaub ntawv. Tab sis cov no piv txwv no tsis tsis muaj excitement, raws li yuav tsum tau qhia rau hauv qab no.

Lub rov tshwm sim ntawm tus xov tooj tshuab

Nws yog ib qhov nyuaj rau hais tias thaum twg, thiab tseem ceeb tshaj, yuav ua li cas cov neeg kawm tau mus ua suav (cia li raws li nws yog tsis yooj yim sua paub paub seb thaum twg thiab, tseem ceeb tshaj, yuav ua li cas lus originated). Nws yog tsuas yog lub npe hu hais tias tag nrho cov ancient civilizations tau lawv account system, ces, lub keeb kwm ntawm cov zauv thiab numbering system originated nyob rau hauv dotsivilizatsionnoe lub sij hawm. Lub pob zeb thiab cov pob txha yog tsis muaj peev xwm qhia rau peb yog dab tsi twb mus nyob rau nyob rau hauv tib neeg lub siab, thiab sau ntawv qhov chaw tseem tsis tau tsim. Tej zaum tus nqi uas yuav tsum tau ib tug txiv neej nyob rau hauv lub division ntawm ntau lawm, los yog ntau npaum li cas tom qab ntawd, thaum lub sij hawm Neolithic kiv puag ncig, xws li, cov kev hloov mus rau ua liaj ua teb, rau cov seem ntawm lub teb plots. Tej theories ntawm cov ntawv no kuj yuav unfounded. Tab sis ib co kev xav tseem yuav ua tau los ntawm kev kawm keeb kwm ntawm ntau hom lus.

Ib co kua nplaum ntawm ib tug ancient tooj system

Qhov tseem zajlus kom starting suav system - tus txheem ntawm lub ntsiab ntawm "ib tug" - "ib tug ntau." Vim hais tias nws yog ib zajlus kom rau peb hais tias nyob rau hauv lub niaj hnub Lavxias teb sab lus, muaj yog tsuas zoo tshaj thiab ntau tshaj. Tab sis nyob rau hauv ntau ancient lus nws kuj yog dual rau xa mus rau ob yam. Nws muaj nyob rau hauv thawj Indo-European lus, xws li ancient Lavxias teb sab. Yog li, lub keeb kwm ntawm tus xov tooj thiab tus xov tooj system pib nrog qhov kev sib cais ntawm lub tswv yim ntawm kev "ib", "ob", "ntau". Txawm li cas los, ntau ncauj lus kom ntxaws numbering tshuab tau tsim nyob rau hauv lub feem ntau ancient civilizations npe hu rau peb.

Mesopotamian cov ntaub ntawv tus xov tooj

Peb yog siv mus rau lub decimal tooj system. Qhov no yog to taub: nyob rau hauv lub ob txhais tes ntawm cov 10 tug ntiv tes. Cuaj kaum, lub keeb kwm ntawm tshwm sim ntawm tus xov tooj thiab tus xov tooj system tau ploj mus los ntawm ib tug yooj yim theem. Mesopotamian numeration system - sexagesimal. Vim hais tias kom deb li deb nyob rau hauv ib teev 60 feeb, thiab ib pliag - 60 vib nas this. Vim hais tias cov xyoo no yog muab faib los ntawm tus xov tooj ntawm lub hlis, ib tug ntau yam ntawm 60, thiab lub hnub yuav muab faib mus rau hauv lub tib cov sij hawm. Chiv nws yog ib tug sundial, uas yog, txhua txhua ib ntawm lawv yog 1/12 ntawm nruab hnub nrig (nyob rau hauv tam sim no-hnub Iraq, nws ntev yog tsis heev varied). Tsuas yog ntau npaum li cas tom qab pib los mus txiav txim qhov ntev ntawm ib teev yog tsis lub hnub, thiab tseem ntxiv 12 teev ntawm lub hmo ntuj.

Nws yog nthuav tias cov ntaubntawv povthawj siv cov qhab nia ntawm lub sexagesimal system, yog hais tias nws yog ib tug zauv - muaj tsuas yog ob tug tej yam tshwm sim (rau xa mus rau ib tug thiab kaum, tsis rau los yog rau caum, namely kaum), cov nuj nqis twb tau los ntawm combining cov tej yam tshwm sim. Nws yog txaus ntshai txawm xav txog tej yam nyuaj npaum li cas nws yog mus rau sau tej loj tus xov tooj nyob rau hauv no txoj kev.

Cov ancient Iyiv tooj system

Thiab zaj dab neeg ntawm tus xov tooj nyob rau hauv lub decimal tooj system, thiab kev siv ntawm ntau yam icons yuav qhia tau rau tus xov tooj pib nrog cov ancient Egyptians. Lawv ua ke lub cim, uas txhais tau tias ib tug, ib puas, ib txhiab, kaum txhiab, puas txhiab, vam thiab kaum lab, yog li qhia rau lub Desired tooj. Xws li ib tug system yog ntau npaum li cas yooj yim tshaj Mesopotamia, uas tsuas yog siv ob tug lej. Tab sis nws muaj ib tug cuab txwv: nws yog ib qhov nyuaj rau sau tus naj npawb, ntau npaum li cas tshaj kaum lab. Txawm li cas los, lub ancient Iyiv civilization, zoo li feem ntau ntawm cov civilizations ntawm lub ancient ntiaj teb no, xws tus xov tooj yog tsis tsum.

Hellenic cov tsiaj ntawv nyob rau hauv lej cim

Lub keeb kwm ntawm European philosophy, science, kev nom kev tswv kev xav, thiab ntau kev lom zem ntau pib nyob rau hauv Ancient Hellas ( "Hellas" - ib tug tus kheej, nws yog preferable rau "tim Nkij teb chaws" invented los ntawm cov neeg Loos). Tsim nyob rau hauv no kev vam meej yog zauv paub. Cov nab npawb ntawm cov Greeks kaw ntawv. Tus neeg ntawv yog txhua ib tug xov tooj ntawm 1 mus rau 9, txhua txhua xyoo caum ntawm 10 mus rau 90 thiab txhua txhua puas los ntawm 100 mus 900. Tsuas ib txhiab tso cai los ntawm tib tsab ntawv raws li lub tsev, tab sis nrog ib tug txawv kos npe rau tom ntej no mus rau tsab ntawv. Lub system cia txawm ntau dua tus xov tooj txhais kuj luv luv inscriptions.

Slavic numbering system raws li lub successor ntawm lub Hellenic

Lub keeb kwm ntawm cov zauv thiab tus xov tooj tshuab yuav tsis tau ua kom tiav tsis muaj ib tug ob peb lo lus hais txog peb cov pog koob yawg koob. Cyrillic, raws li peb paub, nws yog raws li nyob rau hauv lub Hellenic ntawv, thiab yog li ntawd Slavic nuj nqis teev system twb tau raws lub Hellenistic. Ntawm no, ib yam nkaus thiab, ib tug neeg cov tsiaj ntawv txhua sawv cev rau ib tug xov tooj ntawm 1 mus rau 9, txhua kaum 10 mus rau 90 thiab txhua tus puas los ntawm 100 mus 900. Tsuas siv tsis Hellenic cov tsiaj ntawv thiab Cyrillic, los yog Glagolitsa. Muaj kuj yog ib qho kev nthuav feature: nyob rau hauv kev phem ntawm lub fact tias cov Hellenic ntawv thaum lub sij hawm, thiab Slavic los ntawm thaum pib ntawm lawv cov keeb kwm sau los ntawm sab laug mus rau sab xis, Slavic xov tooj tau sau raws li yog hais los ntawm txoj kev mus rau sab laug, hais tias yog, tus tsiaj ntawv designating kaum tso rau ntawm sab xis ntawm cov tsiaj ntawv designating unit, tsiaj ntawv denoting pua pua ntawm cov tsiaj ntawv mus rau sab xis ntawm designating kaum thiab thiaj li nyob. d.

nthab simplification

Hellenic zaum tau mus txog zoo heights. Cov Roman conquest tsis cuam tshuam lawv cov kev tshawb fawb. Piv txwv li, lawv txiav txim los ntawm tsis tseem ceeb pov thawj, Aristarh Samossky 18 centuries ua ntej Copernicus tsim lub heliocentric system ntawm lub ntiaj teb no. Nyob rau hauv tag nrho cov complex suav Hellenic zaum pab lawv cov system ntawm kev sau ntawv xov tooj.

Tab sis rau cov neeg zoo tib yam, xws li ntxeev siab, cov system yog feem ntau yooj yim: yuav siv nws, nws yog tsim nyog los nco ntsoov rau hauv lub zauv tseem ceeb ntawm 27 cov tsiaj ntawv (es tsis txhob ntawm lub suav qhov tseem ceeb ntawm 10 cim uas qhia advanced ntxhais kawm ntawv). Vim hais tias muaj yog ib tug yooj yim to taub system hu ua lub nthab (Attica - Tim Nkij teb chaws cheeb tsam, nyob ib lub sij hawm yog tus thawj coj nyob rau hauv lub cheeb tsam nyob rau hauv Feem ntau, thiab tshwj xeeb tshaj yog nyob rau hauv lub cheeb tsam cov maritime luam, raws li lub peev ntawm Attica twb tus naas ej Athens). Nyob rau hauv no system, tus neeg ntawv tau raug teeb tsa xwb tus xov tooj yog ib tug, tsib, kaum, ib puas, ib txhiab thiab kaum txhiab. Ib tug tag nrho ntawm rau cim - lawv yog cov yooj yim npaum li nco ntsoov thiab dhau txoj laij traders tseem tsis ua.

Roman numerals

Thiab tus naj npawb system, thiab keeb kwm ntawm cov xov tooj ntawm lub ancient Loos, thiab cia li lub keeb kwm ntawm science yog ib tug continuation ntawm Hellenic keeb kwm. Raws li ib lub hauv paus nthab system twb npaum li cas, cia li lub Hellenic cov tsiaj ntawv hloov Latin thiab ntxiv ib daim ntawv tsib caug thiab tsib puas. Nyob rau hauv no txoj suav nyob rau hauv nws treatises zaum txuas ntxiv mus ua cov ntaub ntawv ntawm lub Hellenic system ntawm 27 cov tsiaj ntawv (thiab lawv feem ntau yog ua treatises sau nyob rau hauv Hellenic).

Roman tus xov tooj teev system tsis tau hu ua heev kawg nkaus. Nyob rau hauv kev, nws yog ntau npaum li cas cov tswv yim qub tshaj qhov qub Lavxias teb sab. Tab sis keeb kwm, nws tseem tau cawm rau ib tug par nrog Arabic (thiaj li hu ua) cov nuj nqis. Thiab nco ntsoov qhov no lwm system, nws yog tsis tsim nyog tiaj tus mus thoob siv nws. Nyob rau hauv kev, qhov no yog feem ntau denoted los ntawm Arabic numerals cardinal xov tooj, thiab Roman - ib theem zuj zus.

Greater ancient Indian invention

Cov nuj nqis uas peb niaj hnub siv, muas thaum chiv thawj nyob rau hauv Is Nrias teb. Nws tsis yog lub npe hu thaum zaj dab neeg ntawm tus xov tooj thiab tus xov tooj system ua no zoo kawg li turnaround, tab sis, feem ntau yuav, tsis pub lig tshaj lub V xyoo pua tom qab Tswv Yexus. feem ntau nws kev nyaub siab hais tias nws twb rau cov neeg Idias tau tsim lub tswvyim ntawm xoom. Cov tswvyim no twb paub rau daim ntawv thom nug, thiab lwm yam civilizations, tab sis nws yog tiag tiag ib tug cia li system tso cai rau cov neeg Idias rau muaj xws li nws siab nyob rau hauv lej cim, thiab chaw pib nyob rau hauv lub xam.

Faib qhov Indian system ntawm numeration rau lub ntiaj teb

Tej zaum nyob rau hauv lub IX xyoo pua Indian cov nuj nqis borrowed koom pheej. Thaum Europeans txiaj ntsim ancient cuab yeej cuab tam, thiab nyob rau hauv ib co thaj tsam ntawm ib lub sij hawm txawm txhob txwm tshaj tawm puas lawm nws raws li ib tug pagan koom pheej treasured tau ntawm lub ancient Greeks thiab Loos. Los ntawm cov heev thaum pib ntawm lawv conquests los ua ib tug kub khoom translations ntawm ancient sau phau ntawv mus rau hauv Arabic. Mas los ntawm tracts ntawm as zaum medieval Europeans regained lub cuab yeej cuab tam ntawm ancient xav. Nrog rau cov treatises tuaj thiab Indian numerals, uas lub npe hu ua lub as nyob rau hauv teb chaws Europe. Lawv twb tsis tam sim ntawd txais, vim hais tias feem ntau cov neeg tau tsawg meej npaum li qhov Roman. Tab sis maj mam tsis zauv uas siv cov kos npe rau ntawm yeej ignorance. Coj noj coj ua ntawm cov European industrialized lub teb chaws coj mus rau lub fact tias cov thiaj li hu ua Arabic numerals kis ib ncig ntawm lub ntiaj teb no thiab yog tam sim no siv yuav luag universally.

Binary tus nab npawj system ntawm niaj hnub computers

Nrog lub advent ntawm computers maj ua ib tug tseem ceeb tig ntau qhov chaw ntawm kev txawj ntse. Yog tsis muaj kev zam keeb kwm ntawm tus xov tooj thiab tus xov tooj tshuab. Duab ntawm cov thawj computer Dais me ntsis resemblance yuav niaj hnub ntaus ntawv, cov saib koj nyeem qhov no tsab xov xwm, tiam sis cov ua hauj lwm ntawm ob leeg yog raws li nyob rau hauv lub binary cim, lub code muaj tsuas ntawm zeros thiab sawv daws yuav. cuaj kaum tseem ceeb rau qhov dog dig uas paub hais tias nrog ib tug ua ke ntawm ob cim (ua tau ib lub teeb liab los sis tsis muaj ntawm nws) yuav ua tau heev ua teb thiab txiav (yog hais tias tus coj kev pab cuam) txhais ib tug xov tooj nyob rau hauv lub decimal tooj system rau cov xov tooj nyob rau hauv binary, hexadecimal, shestidesyatishestirichnoy thiab lwm yam system. Thiab nrog rau kev pab los ntawm xws li ib tug binary code rau qhov kev tshuaj ntsuam xwm no tsab xov xwm, uas qhia txog keeb kwm ntawm tus xov tooj thiab tus xov tooj system rau txawv civilizations nyob rau hauv keeb kwm.