Informatics. Ukuguqulwa logic izinkulumo

Umsebenzi ohlongozwayo Sizohlola ngokuningiliziwe umbuzo uguqule izinkulumo okunengqondo. Ngaphezu kwalokho, siphakamisa ukuthi ukuthatha inkambo emfushane logic, okuzokwenza ukubhekana imithetho eyisisekelo futhi imiqondo. Guqula izinkulumo okunengqondo - kunzima kakhulu inkiyankiya yenkinga, uma engazazi zonke ezicashile isihloko.

informatics Yiqiniso abonakale elula ukunikeza injabulo, uma ufundisisa lesi sihloko futhi ufunde imithetho ushintsho, ukuxazulula izinkinga, bese ezilandelwayo izikimu. Sinikeza ukuqala manje.

logic of isayensi

logic Basic - lena ngempela isihloko nzima, ngoba kulotshiwe ukuthi izincwadi eziningi kangaka. Lesi sihloko sizodingida izinto eziyisisekelo imithetho ukuguqulwa wokuboniswa okunengqondo, okungukuthi, ulwazi ezifingqiwe ezimi kakhulu futhi kanzulu. Kuyadingeka ukuba ucabangele enenjongo kakhudlwana Computing ubuchwepheshe kanye isakhiwo izikimu.

Ukuze uqale nalokho yikuphi ukuhlakanipha yini yona? Kubalulekile wazi ukuthi lokhu isayensi ukuthi uhlola amafomu nezindlela yokucabanga. Konke ukubona, ukuzwa noma ingabe, zilalele imithetho. Thina aphonse ibhola endaweni ephakeme - ngaso sonke isikhathi siyandiza phansi njengoba kuncike imithetho yemvelo. Yenza ikhofi ekuseni, ushukela futhi yomile izinto kweso chaza emanzini, ukulalela imithetho yemvelo. Singabantu lapho uxoxa nabangane bakho, wabe izinhlelo zabo: "Uma mina ivikelwe kahle umsebenzi, uthola idiploma", "Angitholanga ukufika ngemoto, njengoba kulungiswa." Bengaboni, sakha zonke izingxoxo zethu, kusekelwe logic nemithetho yayo. Ngakho kungani isayensi logic? Yiqiniso, kulula ukwazi imithetho yayo, uzokwazi ukunquma ngokunembile umphumela umcimbi ngoba abanayo ukwenza nomaphi futhi ingozi.

Nakuba mcabango awulona ngempela inqubo eyinkimbinkimbi Nokho, zingahlukaniswa zibe ezinye izingxenye, noma kunalokho, ifomu (ngosizo okuyinto kukhona isisho yokucabanga):

• imiqondo;
• izitatimende;
• nekunoma
• ubufakazi.

Siphinde ukukunikeza ukuya imisebenzi okunengqondo futhi uguqule izinkulumo okunengqondo. ubuchwepheshe Imininingwane kuyoba ngoba ube mnandi futhi ulula subject, uma ufunda lesi sihloko ngokucophelela.

imisebenzi okunengqondo

Manje sinikeza ngijwayele imisebenzi enengqondo. Ngokuvamile ku amathikithi we esihlanganisiwe isimo ukuhlolwa kwiNgxenye B yonkana imisebenzi yokuguqula logic izinkulumo ku ngezikhawu zezinombolo. Abakwazi ingaxazululwa kungesemehlweni imisebenzi enengqondo.

Uyini umsebenzi oyinhloko yale isayensi? Yiqiniso, ukutadisha izinkulumo okunengqondo (kokubili eziyinkimbinkimbi futhi elula). Indlela kuyinto isiphakamiso nzima? Ngu ukuhlanganisa abavamile, ukuthi kungenxa nemisipha, ezaziwa ngokuthi imisebenzi.

Ubude Kukhona izintambo ezinhlanu:

• kombhala (ie, kuphika, ngokusebenzisa le function, ungathola isitatimende, ngokuphambene nalesi: Ngiya movie namuhla - namuhla angiyi amabhayisikobho);
• disjunction (lo msebenzi uvame ukubizwa kwalokho njengoba okunengqondo, ukuze akwenze kucace, ukunikeza isibonelo esilula zokuphila: "Uma Ngiphethwe ikhanda noma esiswini, ngiyakuya ukuya esikoleni" - le nkulumo iyiqiniso, uma kunakwe okungenani eyodwa nezidingo );
• ngokuhlanganyela (kuvame ukubizwa ngokuthi i-ukubuyabuyelela esinengqondo: "Uma ngizobuya ukugeza izitsha kanye benze izifundo ke ukuhamba nabangani" - le nkulumo kuyoba yiqiniso uma izimo ezimbili ziyabhekelelwa);
• iphuzu (in the logic of lo msebenzi obizwa olandelayo, ngeshwa, akunakwenzeka afanekisela isimo ekuphileni; umsebenzi yamanga ngeke uma into ayefuna ukwenza kodwa ayisebenzanga, kwezinye izimo, umsebenzi kuyoba yiqiniso);
• kulingana emiholweni (noma ukulingana uma izitatimende ezimbili ziyiqiniso noma zingamanga, umphumela sithola iqiniso).

Kubalulekile ukuqaphela ukuthi computer science, noma yiliphi elula luchazwa ngegama bofeleba izinhlamvu zesiLatini. Okulandelayo, kubalulekile ukukhumbula isithebe samaqhuzu ayizinamba lomsebenzi ngamunye. Sicela uqaphele ukuthi akudingekile ukuba ngekhanda kunalokho kanjalo uyokuqonda imisebenzi kuphela.

isithebe samaqhuzu ayizinamba

ngokuhlanganyela

Inkulumo yokuqala (A)	Inkulumo yesibili (B)	Umphumela (C)
L	L	L
futhi	L	L
L	futhi	L
futhi	futhi	futhi

disjunction

A	I	C
L	L	L
futhi	L	futhi
L	futhi	futhi
futhi	futhi	futhi

kombhala

A	I
futhi	L
L	futhi

Okushiwo lapha

A	I	C
L	L	futhi
futhi	L	L
L	futhi	futhi
futhi	futhi	futhi

kulingana emiholweni

A	I	C
L	L	futhi
futhi	L	L
L	futhi	L
futhi	futhi	futhi

Ngaphezu kwalokho, kubalulekile ukuba uqaphele yokuthi itholakala logic wabonisa ngenani 0, futhi inkulumo yeqiniso - the inombolo 1. Ukuze kube lula kuwe, ungafaka isicelo futhi uphawu. Nakani Phawula ukuthi inkulumo ethi zamanga futhi kuyiqiniso e-amatafula ezihlongozwayo emakwe izinhlamvu u- "L" futhi "Mina" ngokulandelana.

isakhiwo

Ngaphambi kokuqhubeka ukuguqulwa wokuboniswa okunengqondo kumele ihlangabezane ukwakhiwa zabo. Noma yimuphi kwakwakhe noma, njengoba kwathiwa ngaphambili, inkulumo eziyinkimbinkimbi inezingxenye ezimbili:

• lokwehlukile kuthiwa okhonjiswe izinhlamvu zamagama;
• Izimpawu ezibonisa umsebenzi futhi axhunyiwe nomunye izinkulumo elula.

Bhala isisho ngolimi algebra logic? Ukuze wenze lokhu, kudingeka benze izinto eziningana:

• ukwabelana bonke bathi ukuba izinkulumo ezilula;
• izinhlamvu selisho lemisuka;
• ukugqamisa ukuthi kukhona ukuhlobana phakathi izinkulumo ezilula;
• ukubhala inkulumo okuholela ngosizo ekhethekile izinhlamvu algebra logic.

Siphakamisa cabangela isibonelo esilula: (Z * F = 5, noma Z * F = 4) no- (Z * F akulingani 5 noma Z * F akulingani 4). Kuyadingeka ukuba bamelele eziguquguqukayo 2. Ngemva kwalokho, sithola amazwi athi (4 noma 5 = 4 = 4) no- (4 akulingani 5 noma 4 akulingani 4). Ngemva kokuhlinzwa, kumelwe ukugqamisa isisho kanye ubudlelwano phakathi kwabo, kufanele uzilungiselele kanje: (Z noma F) no (hhayi Z noma F). Ngemva kwalokho, kudingeka ukuguqula le mibhalo, esikhundleni izitatimende amagugu. Kuleso simo, uma isisho kuyiqiniso, khona-ke kubalulekile ukuba bamelele 1, kungenjalo - 0. Sithola: G = 1 futhi 1. Emva izibalo ezidingekayo, sithola umphumela: G = 1, okungukuthi inkulumo eziyinkimbinkimbi kuyiqiniso.

imithetho

Manje sikumema ukuba sicabangele imithetho imithetho logic namazwi okunengqondo ukuguqulwa. Kubalulekile ukusho ukuthi yiliphi okunengqondo kungenziwa iguqulwe kwenye usebenzisa imithetho enengqondo. Manje sinawo sihlolisise zonke imithetho eziyishumi.

Okokuqala kuhla lwethu - "umthetho ka kuphikisa kabili." Okusho ukuthi, inkulumo ethi "ukungakhethi (hhayi A)" kuyoba inkulumo ethi "A".

umthetho Luchumano kuyinto izibalo, khumbula ke ulula. A + B = B + A, A * B = B * A.

umthetho associative - (D + E) + F = (D + F) + E, umthetho esifanayo sisebenza ukubuyabuyelela okunengqondo.

umthetho Distribution - kuba aphansi ukuvulwa abakaki. Isibonelo: (A + B) * C = (A * C) + (B * C).

umthetho De Morgan: kungekho (A + B) = * Nea Neuve, hhayi (A * B) + = Hea HEB, Hea AimplikatsiyaV = + B, hhayi (AimplikatsiyaV) = A * Neuve.

Idempotency: X + X = C noma C = C *.

constants Ukwehluka: X = 1 + 1 + X 0 = X; X = X * 1, X * 0 = 0.

Okulandelayo thina ukhethe umthetho ukuphikisana, ngokulandela ke, singasho ezothando ezilandelayo: V * = 0 Neuve.

Amaphuzu anengqondo futhi umthetho ukumuncwa, okuyinto in umkhuba simiswe ngalendlela lelandzelako: C + (C * D) = C noma C * (C + D) = C.

Kubalulekile futhi ukukhumbula okunengqondo izinkulumo ukuguqulwa komthetho okuhlukile: (P * E) + (HEC * E) = E noma (C + E) * (HEC + E) = E.

Uma ubheka ngokuningiliziwe, nikhumbule yonke imithetho okwethulwa kulesi sigaba, izinkinga ne ushintsho ngeke ziphinde zenzeke. Okunye futhi okubaluleke ngokufanayo oda ngokubulawa. Nikeza le nto kakhudlwana ukusatshalaliswa efanele imisebenzi oda - kuyisihluthulelo ikhambi lesifanele yenkinga.

Imithetho ukuguqulwa kanye yokuncishiswa, oda izenzo, izibonelo

imithetho enengqondo futhi okunengqondo imithetho izinkulumo ukuguqulwa kulula kakhulu ukukhumbula. Uma ukungabaza iqiniso ngisho omunye wabo, bese uhlola ngokwakho. Ukuze wenze lokhu, udinga ukuchitha imizuzu engu-10 isikhathi sakho futhi wenze etafuleni iqiniso ukuze uthole impendulo.

Manje siphakamisa ukucabangela imithetho logic namazwi okunengqondo imithetho ukuguqulwa izibonelo ezithile. Lokhu kuyadingeka ukuze alungise kahle ulwazi wathola. Gxilani ngokukhethekile isenzo ukulandelana.

Sitshelwe: C + (HEC * E). Kuyadingeka ukuba lula inkulumo. Into yokuqala sinikeza ukuvula kubakaki. Khona-ke sithola le nkulumo elandelayo: (C + HEC) * (C + E). Kufanele kuqashelwe ngokushesha ukuthi kwalokho okunengqondo izitatimende ezimbili okuphambene ukusinika iqiniso. Yini esiyitholayo ngenxa: 1 * (C + E). Nalapha ukuvula kubakaki: (1 * C) + (1 + E). Manje siyaphinda Uyayikhumbula imithetho futhi uthole impendulo: C + E.

Njengoba uke ukubonile, konke ulula. Ukuze kuxazululwe lezi zinkinga kudingeka sikhumbule imithetho ukuthi yabalwa isigaba esedlule. Sinikeza ukuhambisa ukuxazulula izinkinga logic, njengoba lo msebenzi kancane more xaka odlule.

Ukuhlangabezana izinselele

Safike abajwayelene izisekelo zesayensi ngokuthi "indlela yokucabanga", ekuguquleni izinkulumo okunengqondo, sibuyekeze kafushane imithetho efakwe ohlwini. Imisebenzi enzima kakhulu ne ukulungiswa izinkulumo okunengqondo - lo msebenzi. Kubalulekile wazi ukuthi zingaxazululwa ngosizo lwama-agumenti, inkulumo ethi ukuguqulwa noma ithebula indlela. Siphakamisa sihlole eyodwa yazo ngokuningiliziwe.

Abafana abathathu (uCyril, u-Anton futhi bone) babe egumbini elilodwa. Kungazelelwe umama aphume ekhishini ukuzwa umsindo indebe eziphukile. Wagijima waya namadodana akhe, wathi, "Ubani owenzé lokhu?" Impendulo kwaba kanje: Kirill wathi leyo ndebe ayephulanga amathambo, futhi u-Anton; Anton wathi kwenzile Kostya esikhundleni uCyril; Kostya uthi imbangela akuyona Anton. Siyazi ukuthi othile uphawulile ngalokho omunye wabafana yatshela unina iqiniso. Udinga ukuthola ukuthi ngubani waphula inkomishi.

Uma ucabangisisa, impendulo uCyril Anton kungqubuzane, kanye uCyril Kostya. Ngenxa yalokho, awakwazi kokubili kube yiqiniso. Senza lesi siphetho - U-Anton Kostya muntu onitshele iqiniso, bese kuthi uCyril kuyinto ibangelwa lendebe ngobugebengu. Le ndlela iye yasetshenziselwa nokuzindla. Manje ukuphequlula izixazululo inkinga efanayo, kuphela indlela ukuguqulwa inkulumo. Ukuze uqale, sethula izifinyezo:

• KR - inkomishi ngobugebengu uCyril;
• Futhi - indebe sinqamukile Anton;
• K - isephulamthetho wethambo.

Umfana waphendula:

• Cyril - Intamo, A;
• Anton - Necro, K;
• Kostya - Cha.

Ukunikeza ukuze uzwakalise, uma Kostya wayeqambe amanga, futhi uCyril Anton muntu onitshele iqiniso: HEK * A = 1 kanye K * Necro = 1 no = 1. Ukuguqula inkulumo, sithola kuwukuziphikisa: 0 = 1. nokucabanga kwethu ayilungile, kubalulekile ukuba uhlole amanye ezizathwini.

Uma sicabanga ukuthi uCyril wayeqambe amanga, futhi u-Anton futhi Kostya watshela unina iqiniso ke inkulumo ethi ezilandelayo: K * Nea = 1 kanye K = 1 * Necro futhi Nea = 1. Ukwenza Ukuphila Kube Lula inkulumo ethi sithola KR * * Nea HEK = 1. Lokhu kusikisela ukuthi kucatshangwa yethu ilungile, ngempela, uCyril waphula inkomishi futhi eqamba amanga ku umama.

indlela tabular zokuxazulula

Kubhekwe imithetho yikuphi ukuhlakanipha ekuguquleni izinkulumo okunengqondo, ngokuqinisekile zamsiza ukuba sibhekane ngokuphumelelayo umsebenzi, okuyinto uvezwa isigaba esedlule. Manje siphakamisa ukuba ucabangele indlela tabular ka ikhambi lenkinga elandelayo.

Dmitry, Anatoly futhi ULyudmila abalandeli izincwadi leposi, siyazi ukuthi wonke bahlala ezingxenyeni ezihlukahlukene zomhlaba futhi ube izinto zokuzilibazisa ezahlukene. Nquma abahlala yini umuzi nalokho unesithakazelo. Amaqiniso alandelayo:

• Dmitri babengakaze baye Paris, futhi ULyudmila - eRoma;
• Ngakhoke uma umuntu ehlala e-Paris, singafani-movie;
• umlisa ohlala eRoma, bekulokhu vocal;
• ULyudmila ukuya ballet.

Ukuze kuxazululwe le nkinga, kuzomele wenze itafula elincane.

France	Italy	United States		vocals	ballet	ibhayisikobho
			Dmitry
			Anatoly
			ULyudmila

Okulandelayo, ziyadingeka ukunakwa esiphezulu. Konke ufunda e isimo, kumele iboniswe kuleli thebula. Ngokuhamba ukugcwaliswa kuyokhanya kanje:

• Dmitry uhlala eRoma futhi ubelokhu vocal;
• Anatoly uhlala e-Paris futhi ivamile ukuza kuleli ballet;
• ULyudmila - a fan of big cinema, ohlala e-United States.

Sicela waphinda wakhuluma nalaba ababesanda Phawula ukuthi inkulumo ethi kweqiniso imakwe ngenombolo 1 neyamanga - 0 Gcwalisa ithebula nalezi izimpawu, uzoshesha uthole impendulo yombuzo oyithandayo.

Mikroskhematika

Izibonelo ukuguqulwa wokuboniswa okunengqondo ukuthi siye sibuyekezwe, kukhona kubenzima efika kuqala. I amathikithi we esihlanganisiwe isimo isimo ukuhlolwa kungaba wonke ukunikezwa ngesimo chips.

Kubalulekile ukwazi ukuthi wonke amadivayisi digital zisekelwe izakhi logic, okungukuthi, amadivayisi yenza umsebenzi logic.

Sesixoxile mayelana umsebenzi ezifana ngesihlanganiso (ukuphindaphinda okunengqondo). Ivame okhonjiswe uphawu &. Le umsebenzi kuyadingeka ukuze ngokuhlangana yamanani eziningana. Esithombeni ungabona okunengqondo ukubuyabuyelela wesifunda.

disjunction umsebenzi kuyadingeka ukuze uthole ukugcwaliseka disjunction of ezinye zezimiso input. Lapho ebhalela izinkulumo lo msebenzi ngokuvamile yi- u uphawu. Esikhathini isithombe idayagramu.

kombhala umsebenzi kuyinto eyodwa Inkulumo Converter e okuphambene. Esithombeni ungabona kanjani circuit ubukeka "cha."

ISIBONELO yokuncishiswa ifomula №1

Imithetho ngenhla yokuguqula izinkulumo okunengqondo kumele kuvikelwe practice. It Ophishekela lo mgomo, siphakamisa ukuxazulula ngokwakho izibonelo zabo ezimbili nobunzima naphakathi, futhi uma kuqhathaniswa imiphumela kulesi sigaba kwe-athikili.

Uma ungazange kwadingeka isikhathi khumbula ifomula ezinguquko wokuboniswa okunengqondo, ungenza "isikhumbuzi" amancane. Uzobona ukuthi maduze ngeke inhloli yakhe.

Isibonelo: (X-T) * (eHex T) * (M + Akukho). Musa zifa kwisamba, zama ukuxazulula Ngokwesibonelo ngokwakho.

Phakathi lula sithola okufakwe ezilandelayo: T * (M + kungekho) = (T * M) + (T * Ayikho) = (T * NTU) + 0 = (T + 0) * (M + 0) = T * M.

Njengoba ubona kusukela izinkulumo kunalokho eside futhi nzima eziyinkimbinkimbi, sifika emfushane T * M. Uma akakwazanga ukuxazulula bebodwa Kulesi sibonelo, ubheke futhi kuze kube seqophelweni lokuba sabuka ekuguquleni okunengqondo izinkulumo, imisebenzi.

ISIBONELO yokuncishiswa ifomula №2

Kule ngxenye, sinikeza wena lula isisho (E + H) * (E + K). Ake sicabangele isixazululo ngezigaba. Into yokuqala sidinga ukuvula kubakaki, ukukhumbula Yiqiniso kokuqala wezibalo. Ngenxa yalokho, sithola amazwi athi ezilandelayo: E + E * E * N * K * E * N + K. Ngaphezu kwalokho, siphawula ukuthi le nkulumo ingxenye E * E, ukukhumbula idempotency umthetho futhi uguqule entry: E + E * K * N * E * N + K. Esigabeni esilandelayo uguqule we E + E * Ngokusebenzisa bracketing E variable nempahla: A + 1 = 1. Thina ukuthola isisho ezilandelayo: E + H + H * E * K. Ngokulandela phuzu lokugcina fanekiso futhi athathe kubakaki E. Ngenxa yalokho, sithola impendulo: E + H * K.

Nakani yokuthi lo msebenzi kuphela kubonakale kuyinkimbinkimbi efika kuqala. Ukuze "flip kuyabazuma njengemihelo imbewu", udinga nje ukuba ufunde imithetho eyisisekelo logic.