Radix. MISALI nepozitsionnyh lambar tsarin

Yawan tsarin - abin da yake da shi? Har ma ba tare da sanin amsar wannan tambaya, kowannenmu dole a rayuwa tana da numeration tsarin da bai sani ba game da shi. Haka ne, a cikin jam'i! Wannan shi ne ba daya ba, amma da dama. Kafin bada misalai nepozitsionnyh notations, bari mu duba a wannan batun, za mu magana game da positional tsarin, ma.

A bukatar lissafi

Tun zamanin da, mutane suna da bukatar gudu, cewa shi ne lamirinsu sane da cewa kana bukatar ka ko ta yaya bayyana da yawa view of abubuwa da kuma abubuwan da suka faru. Kwakwalwa ya gaya maka cewa kana bukatar ka yi amfani da abubuwa ƙidãya. A mafi yawan dace da yaushe kasance yatsunsu, kuma wannan shi ne m, domin su ne ko da yaushe akwai (tare da 'yan ware).

Wannan yana cikin tsofaffin memba na 'yan adam tanƙwara yatsunsu a zahiri hankali - nuna a fakaice da yawan matattu mammoths, misali. Sunayen irin asusun abubuwa bai wanzu ba, amma kawai na gani image, a kwatanta.

Modern positional lambar tsarin

Adadi System - wani Hanyar (tsari) natsu gwada yawa dabi'u da kuma yawa da wasu haruffa (haruffa ko haruffa).

Ya kamata a fahimci cewa irin wannan positional nepozitsionnyh da gubar kafin bada misalai nepozitsionnyh lambar tsarin. Positional lambar tsarin kafa. Yanzu amfani a fannoni daban daban kamar haka: binary (ya hada da kawai biyu manyan aka gyara: 0 kuma 1) Senary (yawan haruffa - 6), octal (lambobi - 8) duodecimal (goma sha biyu haruffa), HEX (ya hada da goma sha shida haruffa). Kowane jere na haruffa a cikin tsarin farawa a sifili. Modern fasahar kwamfuta dangane da yin amfani da binary code - binary positional tsarin rubutu.

Gidan goma lambar tsarin

Positional ne gaban a sãɓãwar launukansa digiri na gagarumin matsayi, wanda aka located lamba alama. Wannan ne mafi kyau kwatanta ta da gidan goma lambar tsarin. Bayan duk mun saba wa shi daga yara. ÃyõyinSa a cikin wannan tsarin goma: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Take lambar 327. Akwai uku lambobi 3, 2, 7. Kowane daga cikinsu an located a matsayinsu ( wuri). Bakwai daukan matsayin sanya wa guda darajar (raka'a), deuce - da dama, da kuma sau uku - daruruwan. Tun da uku-lambar lamba, saboda haka, matsayi da shi kawai uku.

Bisa ga sama, a uku-lambar gidan goma lambar za a iya bayyana kamar haka: ɗari uku, da kuma ashirin da bakwai raka'a. Kuma muhimmancin (muhimmancin) matsayin kidaya daga hagu zuwa dama, daga wani rauni matsayin (naúrar) zuwa karfi (daruruwan).

Mun kasance sosai dadi Feel a cikin gidan goma positional lambar tsarin. Mu a hannun goma yatsunsu a kan ƙafãfunsu - kamar yadda kyau. Biyar da biyar - don haka, godiya ga yatsunsu, mu saukin tunanin yara da na goma goma. Wannan shi ne dalilin da ya sa akwai mai sauki ne ga yara su koyi da multiplication tebur na biyar da goma. Kuma haka sauki koyi ƙidãya su banknotes, wanda sau da yawa, sau (watau raba ba tare da wata saura) na biyar da goma.

Sauran positional lambar tsarin

Don mamaki da yawa, dole ne a ce cewa ba kawai mu kwakwalwa da aka saba yin wasu lissafin a gidan goma kirgawa tsarin. Har yanzu, mutãne amfani Senary da Duodecimal. Wannan shi ne, a cikin wannan tsarin akwai kawai shida haruffa (a Senary): 0, 1, 2, 3, 4, 5. A da goma sha biyu duodecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 , a, B, inda a - shi ne adadin 10, - da lambar 11 (tun da alama ya zama daya).

Hukunci da kanka. Mun yi imani da lokaci sixes, ba da shi? Sa'a daya - sittin minti (sittin), wata rana - shi ne ashirin da hudu (biyu sau goma sha biyu) shekara - watanni goma sha biyu, da sauransu ... All lokaci ramummuka sauƙi shige cikin six- da duodecimal lambobi. Amma muna haka amfani da su da shi, ba mu ma yi tunanin a karanta lokaci.

Nonpositional lambar tsarin. unary

Kana bukatar ka yanke shi ne abin da shi ne - nepozitsionnyh lambar tsarin. Wannan shi ne irin wani m tsarin, a cikin abin da babu wani matsayi da yawan haruffa, ko da manufa na "karanta" na matsayi ne m. Shi ma yana da da kansa shigarwa dokoki da kuma lissafin.

Ga wasu misalai nepozitsionnyh lambar tsarin. Bari mu koma zuwa zamanin da. Masu amfani bukatar wani asusu da kuma zo da mafi sauki firtsi - nodules. Nonpositional lambar tsarin ne nodular. Daya batu (shinkafa jakar, sa, kirigar ingirici , da dai sauransu) Kidaya, misali, a lokacin da sayen ko sayar da kuma daura kulli a cikin igiya.

A sakamakon haka, da igiya samun kamar yadda da yawa kullin, da yawa bags shinkafa sayi (a matsayin misali). Amma shi ma zai iya zama wani daraja a kan wani katako, itace a kan wani dutse slab, da dai sauransu Wannan lambar tsarin da aka mai suna Lumpy. Yana yana da wani biyu sunan - unary, ko guda ( "Uno" a Latin nufin "daya").

Ya zama shaida akan cewa yawan tsarin - nepozitsionnyh. Bayan duk, game da abin da matsayi suna mun magana game da lokacin da shi (matsayi) daya kawai! Abin mamaki, a cikin wasu sassa na Duniya ne har yanzu a Vogue nepozitsionnyh unary lambar tsarin.

Har ila yau, to nepozitsionnyh lambar tsarin sun hada da:

• Roman (ga rubuce-rubuce da lambobin amfani da haruffa - Latin characters).
• Ancient Masar (kamar Roman, aka kuma yi amfani da alamomin).
• haruffa (amfani da haruffa daga cikin haruffa).
• Kaldiyawa (cuneiform - yi amfani da kai tsaye da kuma prevernuty "sandan");
• Greek (ma ake magana a kai a matsayin haruffa).

The Roman adadi tsarin

Ancient Roman Empire, kazalika da ta kimiyya, ya ci gaba sosai. Romawa suka ba duniya da yawa amfani ƙirƙirãwa na kimiyya da fasaha, ciki har da asusun tsarin. Ɗari biyu da suka wuce, Roman numerals aka yi amfani don nuna a fakaice da yawa na kasuwanci takardu (da haka ne guje wa m).

Roman numerals - misali nonpositional lambar tsarin, an sanar da mu yanzu. Roman tsarin kuma rayayye amfani, amma ba domin ilmin lissafi lissafin, kuma domin tsallaka niyya ayyuka. Alal misali, yin amfani da Roman numerals don nuna a fakaice tarihi kwanakin, karni, juz'i na lambobi, sassan, kuma surori a cikin littafin wallafe. Sau da yawa amfani don ado na Roman ãyõyin dials na sa'o'i. Kuma wani misali na Roman numerals nonpositional radix.

A Romawa sanya lambobin haruffa na Latin haruffa. Kuma da yawan su rubuta wasu sharudda. Akwai jerin key haruffa a cikin Roman adadi tsarin, ta hanyar su, aka rubuta dukan lambobi, ba tare da togiya.

Dokokin na jawo sama da lambobin

The bukata lambar da aka samu ta hanyar kara haruffa (Latin haruffa) da kuma kirga su jimla. Ka yi la'akari da yadda warin rubuta ãyõyi a cikin Roman tsarin, da kuma yadda suke bukatar su zama "karanta". Mun jera ka'idojin samuwar lambobi a cikin Roman adadi tsarin nonpositional.

1. Yawan hudu - IV, an hada biyu haruffa (I, V - daya da biyar). An samu ta hanyar subtracting karami alamar more idan ya tsaya da hagu. Lokacin da karami lamba ne a kan dama, shi wajibi ne don ƙara, sa'an nan samun lambar shida - VI.
2. Wajibi ne a kara biyu m alamar tsaye a gabansa. Ga misali: SS - 200 ne (C - 100) ko da XX - 20.
3. Idan harafin farkon lambar shi ne kasa da na biyu, da na uku a cikin jerin iya zama wata alama ce wanda darajar ne har yanzu karami fiye da na farko. Don kauce wa rikice, mu ba da wani misali: CDX - 410 (gidan goma).
4. Wasu daga cikin ya fi girma lambobi za a iya wakilta a hanyoyi daban-daban, wanda shi ne daya daga cikin downsides na Roman kirgawa tsarin. Ga wasu misalai: MVM (Roman tsarin) = 1000 + (1000 - 5) = 1995 (gidan goma tsarin) ko MDVD = 1000 + 500 + (500 - 5) = 1995. Kuma shi ke ba duk hanyoyi.

ilmin lissafi dabaru

Nepozitsionnyh lambar tsarin - wannan shi ne wani lokacin wani hadadden sa na dokoki domin kafa lambobi, su aiki (aiki a kan su). Ilmin lissafi ayyukan a nepozitsionnyh lambar tsarin - ba sauki ga zamani mutane. Ba mu hãsadar wani Roman lissafi!

MISALI Bugu da kari. Bari mu yi kokarin kara biyu lambobi: XIX + XXVI = XXXV, wannan aiki aka yi a matakai biyu:

1. A farko - kuma dauki wani karami rabo daga cikin lambobin ƙara up: IX + VI = XV (I V da kuma na bayan kafin X "kashe" jũna).
2. Na biyu - ƙara up manyan hannun jari na biyu lambobi: X + XX = XXX.

Subtraction aka yi da ɗan mafi rikitarwa. Rage yawan bukata tsaga a cikin ta bijiro da batun kafa abubuwa, sa'an nan kuma rage-rage, kuma subtracts don rage Kwafin alamomin. Na 500 debewa 263:

D - CCLXIII = CCCCLXXXXVIIIII - CCLXIII = CCXXXVII.

Multiplication Roman numerals. Af, shi wajibi ne in ambaci cewa da Romawa ba da ãyõyi arifmetichekih ayyukan, su kawai, MaganarMu ga su.

Multiplicand ninka adadin da ake bukata domin kowane mutum multiplier alama ce, na'am da dama na fadiwa cewa bukatar da za a folded. A cikin wannan hanya a samar da multiplication na polynomials.

Game da division, da tsari a cikin Roman adadi tsarin ya kuma har yanzu shi ne mafi wuya. Sa'an nan tambaya d ¯ Roman scores - abacus. Don aiki tare da shi musamman horar da mutane (kuma ba kowane mutum ya iya koyon wani kimiyya).

A cikin shortcomings nepozitsionnyh tsarin

Kamar yadda aka ambata a sama, akwai drawbacks, inconveniences a amfani nepozitsionnyh lambar tsarin. Unary ne mai sauki isa ga wani sauki lissafi, amma ilmin lissafi da kuma hadadden lissafin, ba lallai ba ne a duk.

A Roma babu kowa dokoki domin samuwar manyan lambobin da akwai wani rikici, kuma yana da matukar wuya a yi lissafin. Bugu da kari, mafi yawa, wanda za a iya rubuta da Romawa da taimakon da ya Hanyar, ya 100,000.