Tsarin binary ko diatic: Tarihi, wakilci da ƙari

El tsarin binary Yana da matukar mahimmanci a yankin kwamfuta, tunda suna ba da damar fassarar bayanai da ƙimomin lambobi ta hanyoyin fasaha daban -daban, waɗanda za a yi cikakken bayani a cikin wannan bayanin.

Menene tsarin binary?

Tsarin lamba ne wanda ake amfani da shi a cikin lissafi don aiwatar da aikin kwamfuta, kawai suna amfani da lambobi biyu, sifili da ɗaya, kasancewa waɗanda suka zama dole don samun damar wakiltar bayanai gaba ɗaya, wanda yake da girma mahimmanci saboda ana yin aikin waɗannan na'urori ne kawai a cikin matakan ƙarfin lantarki guda biyu, na yanzu da ƙari, yana bayyana gwargwadon adadin lambobin da aka yi amfani da su.

Historia

Gabatarwar farko na tsarin binary Masanin lissafi ne ya yi shi shekaru da yawa da suka gabata, kusa da lokutan ƙarni na uku, kusa da gano lambar sifili, wanda yana da matuƙar mahimmanci don fara wannan ci gaban; sauran muhimman fannoni a cikin labarin shine na I Ching wanda ya yi jerin waɗanda suka ƙunshi ragowa uku da lambobi binary shida, waɗanda aka yi amfani da su don yin haɗin binary.

Akwai shirye-shirye iri-iri daga karni na 1605, wanda Shao Yong ya yi wanda ya gabatar da umarni daga wannan fahimta, halayyar samun tsari daga sifili zuwa sittin da uku, yana nuna yadda dabarar tsara wannan tsari take, kamar yadda shekaru suka shude , an nuna mahimman batutuwa ga batun, a shekara ta XNUMX Bacon Francis ya ba da bayani kan yadda za a iya gabatar da haruffan cikin lambobi biyu.

An yi wallafe -wallafen littattafai waɗanda aka jaddada ta hanyar ba da bayanin tsarin binaryar, an kuma yi rubuce -rubuce inda aka yi amfani da nau'ikan alamomi, duka na Sinanci da na lissafi, ta amfani da daidai 0 da 1 kamar yadda aka nuna a yau, sannan ta shekarar 1854 da aka buga George Boole ne ya yi bayanai, inda ya yi bayanin tsarin hankali da ake kira Boolean Algebra.

An kafa wannan tsarin azaman mahimmin mahimmanci a cikin ci gaban da'irar nau'in lantarki, ya ba da gudummawa da yawa na irin wannan aikin, don haka yana da mahimmanci a san game da tsarin binary da maki daban -daban da ke da alaƙa.

An gabatar da wakilcin binary a matsayin babban ɗan takara a cikin ci gaban wannan yanki, idan kuna da sha'awar hakan muna ba da shawarar karanta game da juyin halitta na kwamfuta.

Aplicaciones

Kowane ɗayan mahimman fannonin wannan batun an yi amfani da shi don dalilai daban -daban ta ƙwararrun waɗanda suka sadaukar da kai, daga cikinsu akwai mai suna Claude Shannon wanda ya gabatar da tafsirinsa yana amfani da Algebra na Boola da lissafin binary, kasancewa mai mahimmanci saboda shine farkon lokacin da aka yi amfani da sauyawa da relays, shekaru bayan haka Stibitz George ya gina ginin kalkuleta ta amfani da relays.

A cikin 1940 an gabatar da haɓakawa don ƙirƙirar ƙididdigar lissafi, yana nuna waɗanda ke amfani da lambobi masu rikitarwa, waɗanda aka nuna ta hanyar nuna tasirin su, yayin da aka yi ƙarin aiki a kai, an tura nau'ikan umarni daban -daban zuwa kalkuleta, ta hanyar amfani da wayar layi.

A halin yanzu ana amfani da tsarin binary don dalilai daban -daban, tunda ya dogara ne akan takamaiman aiki a fasaha, a yau an nuna ci gaba a hanya mai kyau, saboda haka, ana gabatar da dacewar sa akai -akai, daga cikin manyan mahimman bayanai shine shirye -shiryen na microprocessors, kasancewa masu fa'ida sosai a cikin lissafi.

Sauran aikace -aikacen sun kasance ɓoye bayanan, ga waɗanda ke buƙatar babban sirri, tunda suna da sirri, amfani da tsarin binary ya kasance mai tasiri, samun damar canja bayanai daban -daban a cikin nau'ikan tsarin ya kasance fa'ida ga lokutan. , kazalika yana da alaƙa kai tsaye da aikace -aikacen ladabi don a sami sadarwa ta hanyar dijital.

An gabatar da tsarin binary a cikin haɓakawa da haɓaka fasaha, kamar yadda abin da ake lura da shi a halin yanzu, muna ba da shawarar karantawa misalan fasahar dijital.

Wakilci

Kamar yadda aka haskaka a sama, a cikin tsarin binary kawai 0 da 1 ana amfani da su, adadi ne guda biyu waɗanda wasu lambobi ke wakilta, kamar ragowa, tunda suna nuna takamaiman mahallin don fassarar sa daidai, yana ba da cikakken misalai masu zuwa don fahimtar kowane jerin:

Aikin alamomin zai zama mai mahimmanci, a cikin kwamfuta kowanne lamba da aka samu ana samun sa ta wani nau'in ƙarfin lantarki, wannan kuma yana iya dangantaka da wasu nau'ikan maki kamar polarities, magnetism, amma komai zai dogara ne akan alamomin da ake amfani da su, ba a iya ganin su cikin sauƙi, saboda wannan dalilin wakilci yana da mahimmanci kuma ana amfani da ƙimar lambobi na Larabci.

Gabaɗaya, ana amfani da 0 da 1, amma ana iya aiwatar da wasu nau'ikan wakilci, tunda yana da wasu bambance -bambancen, saboda haka, ya zama dole la'akari da waɗannan abubuwan:

• Binary 100101, wannan tsari ne da aka saba amfani dashi.
• 100101b, wannan wani wakilci ne don nuna nau'in tsarin binary.
• 100101B, ana gabatar da shi daidai da shari'ar da ta gabata.
• Bin 100101, prefix ne da ake amfani dashi don tsarin nau'in binary.

Juyawa

Ofaya daga cikin abubuwan da ya kamata a ba da haske shine juzu'in da aka yi tsakanin binary da decimals, akwai lokuta daban -daban, waɗanda suka bambanta a wasu fannoni, don haka, dole ne a yi la’akari da kowane daki -daki don tsarin aiwatarwa ya dace kuma ba mai rikitarwa bane. don yin, ana nuna masu zuwa.

Ƙasa zuwa binary

Na farko, ana la’akari da ƙimar lambar ƙima, wanda dole ne a raba ta biyu, sakamakon kuma dole ne a raba ta biyu, kuma za a yi amfani da wannan tsari har sai an sami lambar da ba ta wuce biyu, don sauƙaƙa fahimta, za a haskaka misalai mai sauƙi, domin ku ga kowane matakan da dole ne a cika domin wannan hanya mai sauƙi ta cika.

• Kuna samun lambar binary 131.
• Raba 131 da biyu yana ba da sakamakon 65 tare da ragowar 1.
• Sannan ana ci gaba da raba kashi biyu kuma ana samun lambar 32, kuma tare da ragowar 1.
• Ya ci gaba da 32 cewa lokacin raba kashi biyu shine 16, yana gabatar da ragowar 0.
• Sannan 16 tsakanin biyu yana ba da 8, tare da ragowar 0.
• Takwas ya kasu kashi biyu huɗu ne, ragowar da aka samu shine 0.
• 4 an raba ta sakamakon biyu cikin biyu, wanda ke nufin ragowar shine 0.
• Kuma biyu tsakanin biyu abu ɗaya ne, saboda haka ragowar shine 0, don kammala wannan aikin, ana ɗaukar kashi na ƙarshe cewa ɗaya ne, wannan ya zama dole don samun damar kafa oda daidai.
• An kafa tsarin koma baya, daga ragowar na ƙarshe zuwa na farko, wanda ke nufin tsarin binary na 131 shine 10000011.

Hanya ce mai sauqi don amfani, kowane asusun dole ne a aiwatar da shi yadda yakamata don binciken da aka yi ba kuskure bane, duk da haka, akwai kuma wasu hanyoyin da zasu ba da damar samun waɗannan sakamakon, amma gaba ɗaya ana ɗaukar wannan mafi sauƙi don nema.

Yanki (tare da ƙima) zuwa binary

Wannan wani lamari ne da dole ne a yi la’akari da shi don juyawa, idan aka sami lamba tare da ƙima goma yana yiwuwa a aiwatar da canjin sa zuwa lambar binary, don wannan, dole ne a yi la’akari da wasu abubuwan da za a yi amfani da su waɗanda za su ba da damar zama za'ayi a cikin tsari daidai.

• Da farko yin la'akari da ɓangaren lamba na adadin adadi, tunda an canza wannan da farko, a cikin yanayin cewa 0 ko 1 ne, to a cikin tsarin binary zai kasance iri ɗaya.
• Sannan ana la'akari da ɓangaren juzu'in, don kowane ɗayansu dole ne a aiwatar da ninkawa ta lamba ta biyu, idan sakamakon ya wuce lamba ɗaya to dole ne a sanya 1, tunda ƙimar binary ce, a cikin yanayin da yake kasa da haka yakamata a sanya 0.
• A ƙarshen kowane ninki da yawa sannan sakamakon da aka samu azaman ƙimar binary dole ne a yi oda bisa ga samun su.

Ba hanya ce mai rikitarwa ba, a zahiri ana ɗaukarta ɗayan mafi sauƙi kuma mafi sauri, saboda haka, don gujewa rudani, za a ba da wasu misalai waɗanda ke ba da damar fahimtar ta da sauri, kasancewa masu zuwa:

• Yana da lambar adadi mai zuwa: 0,3125.
• Tun da lambar lamba 0, ana sanya shi a cikin hanya ɗaya don tsarin binary kuma ana ci gaba da ninkawa.
• Haɗawa da biyu yana ba da ƙimar 0,625.
• Yanzu ci gaba da ninka ƙimar da aka samu ta biyu kuma sami 0,5.
• Hakanan an cika wannan tsari kuma an sami ƙimar 1.
• Sannan bisa ga kowane sakamakon da aka samu, la'akari idan ya fi 1 ko a'a, juyawa zuwa binary shine 0,0101.

Yanzu, za a gabatar da shari'ar daban, don ku sami ra'ayin abin da za ku yi lokacin da lamba ba 0 ko 1 ba, yakamata a yi amfani da waɗannan masu zuwa:

• Lambar adadi don canzawa shine 5,5.
• Tun da lambar lamba 5 ce, juyawa zuwa binary dole ne ya haɗa da 101.
• Ci gaba da ninka lambar adadi 0,5 ta biyu, samun sakamakon 1.
• Sannan dole ne a sanya lambar binary ɗin cikin tsari, kasancewa 101,1.

Ya zama dole a yi amfani da jujjuyawar ta hanyar da ta dace, wato, wanda ya dace da shari'ar, tunda ba duka ake aiwatar da su iri ɗaya ba, gwargwadon abin da kuke son samu, wasu ƙa'idodi da maki waɗanda ke da alaƙa da ƙimar binary. Kazalika da adadi, ba da damar juyawarsu ta yiwu ta la'akari da dukkan bangarorin da suka fito daga tsarin binary.

Binary zuwa decimal

Sauran hanyoyin da za a iya aiwatarwa shine jujjuya lambar binary zuwa adadi, wannan ya bambanta da shari'o'in da suka gabata, don haka dole ne ku yi taka tsantsan, amma kuma daidai yake da sauƙi.

• Dole ne a ɗauki lambar binary daga dama zuwa hagu, don amfani da ninka.
• Kowane lambobi dole ne a ninka shi biyu kuma dole ne a ɗaga shi zuwa ikon da zai biyo baya.
• Lokacin samun kowane sakamakon ninnin abubuwa, dole ne a ƙara waɗannan kuma adadin da aka samu za a ɗauka azaman ƙima.

Binary zuwa decimal (tare da ɓangaren ɓangaren binary)

Don wannan yanayin, ana ɗaukar lambar binary, in ba haka ba, ana la'akari da gefen hagu na farko, kuma ana amfani da ninkawa ta biyu, wanda dole ne a ɗaga shi zuwa ikon da ke ci gaba da jujjuyawar sa, bayan an yi kowane ɗayan waɗannan. za a ƙara, kuma lambar da aka samu za ta zama ƙima.

Ayyuka

Lambobin binary na iya samun aikace -aikace daban -daban ko dai don ƙari, ragi, ninkawa, ƙima, ba a samun wannan daidai da lambobi na halitta don wasu lokuta, saboda haka, yana da mahimmanci a san musamman yadda ake gudanar da ayyuka a cikin tsarin binary.

Additionari

Don aiwatar da aikin ƙari a cikin tsarin binary, yana da mahimmanci a bi wasu ƙa'idodi kuma a bi ƙa'idodin da ke ba da damar yin lissafin daidai, ana ɗaukarsa hanya ce mai sauƙi, don haka an nuna cewa ƙa'idodin sune kamar haka:

• 0 + 0 = 0.
• 0 + 1 = 1.
• 1 + 0 = 1.
• 1 + 1 = 10.

Waɗannan su ne mahimman mahimman abubuwan da dole ne a sadu da su don ƙarin aikin da ya dace da za a aiwatar da shi tare da lambobin binary, muddin aka ɗauki kulawa sosai don yin waɗannan ƙididdigar, gabaɗaya aikin gabaɗaya za a yi shi cikin sauri da sauƙi, don har yanzu fahimtar ƙarin game da shi, za a nuna misali kamar yadda tsari yake.

• Misali, ana yin jimlar 0011101 da 1101011.
• Dole ne a aiwatar da kari daga dama zuwa hagu, saboda haka, ana sanya adadi ɗaya a ƙasa ɗayan don amfani da jimlar kowane shafi.
• Sannan, bin ƙa'idodi, aikin zai fara, da farko 1 + 1 = 10, saboda haka, dole ne ku sanya 0 kuma ku ɗauki 1.
• Ci gaba da ƙara 1 wanda ake ɗauka tare da 0, inda 1 + 0 = 1 kuma an ƙara wannan sakamakon tare da 1 daidai, saboda haka shine 1 + 1 = 10, an sanya 0 kuma an dawo 1.
• Ci gaba da shafi na uku, ƙara 1 wanda aka ɗauka tare da 1 na farkon kalma, kasancewa 1 + 1 = 10, to yanzu ana amfani da 10 + 0 = 10, kamar yadda a lokuta da suka gabata, an sanya 0 kuma yana ɗauka 1.
• Ga shafi na huɗu, da farko shine 1 + 1 = 10 sannan 10 + 1 = 11, za a sanya ɗayan kuma a ɗauki ɗayan.
• A cikin shafi na gaba to zai zama 1 + 1 = 10 sannan 10 + 0 = 0, sanya sifili kuma ci gaba da ɗaukar 1.
• Shafi na shida yana farawa da ƙara 1 + 0 = 1 kuma daga can 1 + 1 = 10, an maye gurbin 0 kuma an ɗauki 1.
• Ga shafi na ƙarshe, sannan an ƙara 1 + 0 = 1 sannan 1 + 1 = 10, sannan na ƙarshe idan an sanya 10.
• Ta hanyar kammala wannan hanyar don yin jimlar, ana samun sakamakon 10001000, kasancewa mai sauƙin aiwatarwa, koyaushe dole ne ku san adadin da ake ɗauka, don haka ku guji kurakurai.

Ragewa

Don aikin ragewa, dole ne a yi la’akari da wasu ƙa’idoji, kasancewar sune:

• 0-0 = 0.
• 1-0 = 0.
• 1-1 = 0.
• 0-1 = 1 kuma yana ɗaukar 1.

Don wannan, ana amfani da misalin tare da lambobi masu zuwa, 001100011 da 000011110, haka kuma dole ne a yi shi daga dama zuwa hagu, ana amfani da ƙa'idodi a cikin kowane ginshiƙai kuma ana samun sakamakon 001000101, don isa wannan sakamakon An gudanar da aikin kamar haka:

• A cikin shafi na farko shine 0, yana fitowa daga 1-0 = 0.
• A na gaba, ana amfani da 1-1 = 0.
• Rage na uku shine 0-1 = 1, kuma banda wannan yana ɗaukar 1.
• Ga shafi na huɗu, da farko ana ɗaukar cewa ana ɗaukar 1, sannan dole ne a yi amfani da 1-0 = 1, sannan ana ɗaukar 1 don na gaba, sannan ana amfani da 1-1 = 0, wanda shine wanda dole ne a sanya a cikin sakamako.
• Yanzu a cikin na biyar ana amfani da shi daidai da na shafi na huɗu, yana samun 0 a sakamakon.
• A na gaba, ana yin 1-1 = 0 sannan 0-0 = 0, dole ne a sanya 0.
• Shafi na bakwai shine 1-0 = 1.
• Sannan ya bi 0-0 = 0.
• Kuma a ƙarshe, 0-0 = 0.
• Sabili da haka, yin kowane ɗayan waɗannan ginshiƙan domin yana haifar da 001000101.

Yawaita

Don yanayin samfurin tare da lambobi na binary, babu takamaiman dokoki da aka gabatar don wannan aikin kamar yadda yake a cikin ƙari da ragi, don aiwatar da ninka dole ne a yi amfani da aikin kamar yadda aka yi tare da lambobi goma, saboda haka, a wannan yanayin babu canje -canje, babu sauran ƙarin ilimin da ake buƙata.

Raba

Haka kuma yana faruwa tare da adadin lambobi na binary, ƙa'idodin da dole ne a cika su, tsarin da dole ne a yi amfani da shi iri ɗaya ne da wanda aka aiwatar a cikin rarrabuwa ta yau da kullun tare da lambobi goma, kamar yadda ake ninkawa, babu canje -canje a cikin aikin da aka yi amfani da shi.