Informatics. Ukuguqula iZimo zeBoolean

Ezi nkonzo ziya kuvavanywa ngokweenkcukacha lo mbuzo inguqu enengqondo amabinzana. Ukongeza, sicebisa ukuba izifundo ezifutshane kwi logic, eya kulungisa imithetho esisiseko namabinza. Guqula amazwi ubhalo - zako yinkqubo enzima, ukuba ungayazi yonke bokuqonda zesifundo.

Ikhosi yokwazisa luza kukhangeleka lulula awuyolise, ukuba ufunda ngenyameko eli nqaku ufunde imithetho kunye nemithetho zenguqu, zokusombulula iingxaki, nokuzoba up amacebo. Sinikezela ukuqala ngoku.

anengqondo kwesayensi

logic Basic - oku kakhulu isifundo nzima, kuba kubhaliwe kwathiwa iincwadi ezininzi kangaka. Eli nqaku liza kuxubusha iziseko yemithetho yotshintsho amabinzana ubhalo, oko kukuthi, ulwazi ezimi kwaye kanzulu. Kuyimfuneko ukuqwalasela nenjongo technologies computing neenkqubo zokwakha.

Okokuqala into logic yintoni na ukuba? Kubalulekile ukuba uqaphele ukuba esi isayensi uhlolisisa iifom kunye neendlela nokuqiqa. Yonke into ukubona, ukuva okanye ngaba, ukuthobela imithetho. Siphosa ibhola kubude - usoloko iimpukane phantsi ngokuxhomekeke kwimithetho physics. Yenza i ikofu kusasa, dibanisa iswekile kunye owomileyo izinto nangoko ukunyibilika emanzini, yokuphulaphula imithetho physics. Thina Xa uhleli nabahlobo, babelane izicwangciso zabo: "Ukuba ndithe ikhuseleke kakuhle umsebenzi, ufumana yidiploma", "akazange ukufumana ukuba fika ngemoto, njengoko kulungiswa." Ngaphandle bengaboni, sisakha zonke iincoko zethu, livela ekuqiqeni kunye nemithetho yayo. Ngoko kutheni isayensi i-logic? Kakade ke, esazi imithetho yayo, uya kukwazi ukujonga ngokuchanileyo kwisiphumo sesenzo ngokuba abanako ukwenza efunisela nobungozi.

Nangona yokucinga kakhulu yinkqubo engelula, nangona kunjalo, oku kwahlulwa-hlulwa ibe amanye amacandelo, hayi kanye mandithi, le fom (ngoncedo apho kukho yimbonakaliso ingcinga):

• nesigama;
• iingxelo;
• engenantandabuzo
• bungqina.

Sicela ukuba uye imisebenzi ubhalo kunye nokutshintsha amabinzana ubhalo. technology Ulwazi luya kuba ube mnandi kwaye kakhulu ilula isifundo, ukuba ufunda ngenyameko eli nqaku.

imisebenzi enengqondo

Ngoku sinikela aqhelane nemisebenzi logic. Amaninzi kule amatikiti luhlolo karhulumente elimanyeneyo kwiCandelo B kuzo imisebenzi lokuguqula amabinzana logic ibe kumathuba ngamanani. Abanakukwazi ukuba ingalungiswa ngaphandle ulwazi imisebenzi logic.

Yintoni umsebenzi iphambili yale isayensi? Kakade ke, izifundo amabinzana ubhalo (zombini entsonkothileyo kunye ezilula). Njani i sicelo nzima? Xa ukuhlanganisa eziqhelekileyo, oko kukuthi ngenxa nemisipha, ezaziwa ngokuba imisebenzi.

Total Kukho ngeentambo ezintlanu:

• inversion (ukutsho oko, kuphika, ngokusebenzisa lo msebenzi, ungafumana ingxelo, echasene nale: ndisiya bhanya namhlanje - namhlanje mna andikanyuki, ndiye-bhanya);
• disjunction (lo msebenzi kudla ngokuthiwa Ukongeza banengqondo, ukuze ndiyibonakalalise, ukunika umzekelo olula wobomi: "Ukuba Ndinentloko okanye isisu, mna ndiye esikolweni" - eli binzana kuyinyaniso, xa kuthathelwa ingqalelo ubuncinane omnye wemiqathango );
• beqhuba (ukubizwa ngokuba phindo ubhalo: "Ukuba Ndiza ahlambe izitya aze enze izifundo, emva koko ahambe kunye nabahlobo" - eli binzana kuya kuba njalo xa iimeko ezimbini kuthathelwa ingqalelo);
• kukusulela (kwi-logic kwalo msebenzi kuthiwa ngokulandela, ngelishwa, akunakwenzeka ukuzekelisa meko ubomi; umsebenzi lobuxoki aya kuba xa kukho into efuna ukuyenza, kodwa zange isebenze, kwezinye iimeko, umsebenzi uya kuba njalo);
• ukulingana (okanye ukulingana ukuba iingxelo ezimbini ziyinyaniso okanye bubuxoki, isiphumo siya ukufumana inyaniso).

Kubalulekile ukuqaphela ukuba kwinzululwazi yekhompyutha, naliphi na ibinzana elula luchazwa neleta elikomkhulu oonobumba Latin. Emva koko, kuyimfuneko ukuba ukukhumbula itafile inyaniso umsebenzi ngamnye. Nceda qaphela ukuba akukho mfuneko ngentloko kunokuba uya kuqonda kuphela imisebenzi.

inyaniso iyidandalazise

beqhuba

Ibinzana lokuqala (A)	Elesibini Ibinzana (B)	Isiphumo (C)
L	L	L
and	L	L
L	and	L
and	and	and

disjunction

A	the	C
L	L	L
and	L	and
L	and	and
and	and	and

inversion

A	the
and	L
L	and

Kuyacaca

A	the	C
L	L	and
and	L	L
L	and	and
and	and	and

ukulingana

A	the	C
L	L	and
and	L	L
L	and	L
and	and	and

Ngaphezu koko, kubalulekile ukuqaphela into yokuba ubuxoki kwi logic kuboniswe linani 0, kwaye ibinzana lokwenyaniso - lelo nani 1. Kuba lula lwakho, ungenza isicelo kwaye iphawu lokwengeza okanye lokucutha. Nikelani ingqalelo into yokuba ibinzana lobuxoki ayinyaniso kwiitheyibhile ecetywayo ziyaphawulwa ngokuzibhala oonobumba "L" yaye "Mna" ngokulandelelana kwazo.

isakhiwo

Ngaphambi kokuqhubeka ukuguqulwa amabinzana ubhalo kufuneka ihlangane ukwakhiwa yabo. Nayiphi ezimbaxa okanye, njengoko nditshilo ngaphambili, ibinzana complex iqulathe iinxalenye ezimbini:

• eziguquguqukayo zibonakaliswe yi oonobumba be-alfabhethi;
• Iimpawu ezibonisa umsebenzi kwaye uqhagamshele ngamnye nezinye izinto ezilula.

Bhala ibinzana ngolwimi algebra ekuqiqeni? Ukuze wenze oku, kufuneka wenze izinto ezininzi:

• wabelane zonke wathi amabinzana elula;
• oonobumba libhekisela ezo zinto;
• zibonisa unxulumano phakathi amabinzana ezilula;
• bhala amazwi ngenxa ngoncedo ababasebenzisi algebra ekuqiqeni.

Sicebisa ukuba siqwalasele umzekelo olula: (Z * F = 5, okanye Z * F = 4) kunye (Z * F akalingani-5 okanye Z * F akalingani 4). Kuyimfuneko ukuba abambele yezahlukileyo 2. Emva koko, sifumana amazwi (4 okanye 5 = 4 = 4) kunye (4 akalingani-5 okanye 4 akalingani 4). Emva kokuba ahlinzwe, mandiyiqaqambise ibinzana elithi kwaye ubudlelwane phakathi kwabo, kufanele ilungiswe ngolu hlobo lulandelayo: (Z okanye F) kunye (hayi Z okanye F). Emva koko, kufuneka ukuba ukuguqula eli khasethi, kufakwe iingxelo amanani. Xa kunjalo, ukuba binzana kuyinyaniso, ngoko kuyimfuneko ukuba kufakwe endaweni 1, ngenye indlela - 0. Sifumana: G = 1 1. Emva izibalo kuyimfuneko, siye sifumane iziphumo: G = 1, oko kukuthi ibinzana imbaxa kuyinyaniso.

imithetho

Ngoku siyakumema ukuba uqwalasele imithetho imithetho logic kunye amabinzana ubhalo inguqu. Kubalulekile ukukhankanya ukuba nayiphi na imbonakalo ubhalo inokujikwa ibe omnye usebenzisa imithetho ekuqiqeni. Ngoku sihlolisise yonke imithetho elishumi.

Okokuqala kuluhlu lwethu - i "umthetho kuphika kabini." Oko kukuthi, ibinzana elithi "akukho (hayi A)" Kuya kuba amazwi "A".

umthetho ngokunxibelelana na kwimathematika, khumbula ukuba ilula. A + B = B + A, A * B = B * A.

umthetho associative - (D + E) + F = (D + F) + E, lo mgaqo uyasebenza kwi-phindo esisengqiqweni.

umthetho Distribution - yinto ipharenthensisi yokuvula iyevakala. Umzekelo: (A + B) * C = (A * C) + (B * C).

umthetho De Morgan esithi: akukho (A + B) = * Nea Neuve, hayi (A * B) + = HEA HEB, HEA AimplikatsiyaV = + B, kungekhona (AimplikatsiyaV) = A * Neuve.

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

constants engalawulwa ngulo mthetho: X = 1 + 1 + X 0 = X; X = X * 1, X * 0 = 0.

Okulandelayo thina ukhethe umthetho zingqubanayo, ngokulandela kuyo, singatsho inxaki ilandelayo: V * = 0 Neuve.

Anengqondo kunye nomthetho edalwayo, nto yokwenza ngolu hlobo lulandelayo: C + (C * D) = C okanye C * (C + D) = C.

Kwakhona kubalulekile ukukhumbula ubhalo conversion amabinzana ngaphandle komthetho: (P * E) + (HEC * E) = E okanye (C + E) * (HEC + E) = E.

Ukuba ujonga ngokweenkcukacha, niyikhumbule yonke imithetho thaca kweli candelo, iingxaki kunye inguqu soze kuya kwenzeka. Enye into ebalulekileyo ukuze ngokubulawa. Nika into ingqalelo engakumbi nokwabiwa ngokufanelekileyo kwemisebenzi yocwangco - ngundoqo isicombululo oluchanekileyo ngxaki.

Imithetho kunye nemithetho lenguqu lula, umyalelo iintshukumo, imizekelo

imithetho ubhalo kunye namaxabiso okomqondo imithetho amazwi inguqu Kulula kakhulu ukuba ukukhumbula. Ukuba uyathandabuza inyaniso namnye kubo, koko hlola ngokwakho. Ukwenza oku, umele uchithe 10 imizuzu yakho uzenzele inyaniso netafile impendulo.

Ngoku sicebisa ukuba siqwalasele imithetho ekuqiqeni amabinzana ubhalo imithetho inguqu ngemizekelo ethile. Oku kuyimfuneko ukuze ulungise kakuhle ulwazi ezifunyenweyo. Nika ethile ingqalelo kwi nolandelelwano.

Sinikwe: C + (HEC * E). Kuyimfuneko ukuba kwenziwe lula ibinzana. Into yokuqala sinikela ukuvula kwizibiyeli. Emva koko afumane ibinzana ilandelayo: (C + HEC) * (C + E). Kufuneka kuqatshelwe nangoko ukuba kongezwe ubhalo zeengxelo amabini malunga kusinika inyaniso. Yintoni sifumana ngenxa yokuba: 1 * (C + E). Uzivulu kwizibiyeli: (1 * C) + (1 + E). Ngoku kanye kwakhona ukukhumbula imithetho uze ufumane impendulo: C + E.

Njengoko sibonile, zonke ilula. Ukusombulula ezi ngxaki kufuneka sikhumbule imithetho akade kwicandelo odlulileyo. Sinikezela ukuba afudukele ukusombulula iingxaki logic, njengoko lo msebenzi ngakumbi kancinane xaka wangaphambili.

Ukwanelisa mngeni

Saba wayeqhelene iziseko inzululwazi ebizwa ngokuba 'logic', inguqu amabinzana ubhalo, siya ngokufutshane ngokutsha imithetho edwelisiweyo. Le misebenzi inzima kulwenziwo amabinzana ubhalo - lo msebenzi. Kubalulekile ukuqaphela ukuba ingasombululwa ngoncedo lokuphikisana, ibinzana ukuguqulwa okanye indlela itafile. Sicebisa ukuba siqwalasele omnye ngokweenkcukacha.

amakhwenkwe amathathu (uCyril, Anton nethambo) kweli gumbi elifanayo. Ngequbuliso uMama ngaphandle ekhitshini eve isandi eyaphukileyo indebe. Wabaleka oonyana bakhe, wathi, "Ngubani lo usenze le nto?" Impendulo ngolu hlobo lulandelayo: KIRILL wathi indebe uwaphule akukho amathambo, kunye Anton; Anton uthe wenza Kostya kunokuba uCyril; Kostya uthi ngumtyholwa ayikho Anton. Siyayazi ukuba kukho umntu omnye wabafana waxelela unina inyaniso. Kufuneka ukuba ngubani waphula ikomityi.

Ngokusengqiqweni, impendulo uCyril Anton iyaphikisana, kwakunye Cyril Kostya. Ngenxa yoko, abanako bobabini iyinyaniso. Senza isiphelo zilandelayo - Anton kunye Kostya unixelele inyaniso, yaye uCyril nguye ngumtyholwa indebe ezaphukileyo. Lendlela yayisetyenziswa ndiyacamngca. Ngoku lokhangelo lwencwadi izisombululo ingxaki efanayo, kuphela indlela ukuguqulwa nkulumo. Okokuqala, sisithi thaca izifinyezo:

• Korea - ndebe eyaphukileyo uCyril;
• Kwaye - indebe yaphukile Anton;
• K - umenzi wobubi wethambo.

Lo mfana waphendula wathi:

• Cyril - Neck, A;
• Anton - Necro, K;
• Kostya - Nope.

Offer ukwenza ibinzana, ukuba Kostya amanga, kunye uCyril kunye Anton wabaxelela inyaniso: HEK * A = 1 no K * necro = 1 A = 1. Ukuguqula mazwi, sifumana yintswela: 0 = 1. Ingqikelelo yethu ayilunganga, kuyimfuneko ukuhlola ezinye iingqikelelo.

Xa sicingela ukuba uCyril uqambe, kunye Anton kunye Kostya waxelela umama wakhe inyaniso, ngoko ibinzana zilandelayo: K * Nea = 1 K = 1 * Necro kunye Nea = 1. Lula ibinzana sifumana Korea * * Nea HEK = 1. Oku kubonisa ukuba vekeleke lethu ilungile, eneneni, uCyril waqhekeza ikomityi kunye Ndingaxoki nomama wam.

indlela Tabular ukusombulula

Ingqalelo imithetho ekuqiqeni kunye nokuguqulwa ubhalo amabinzana, ngokuqinisekileyo wasinceda ukuba ukumelana nomsebenzi, leyo linikwa kwi edlulileyo kwicandelo. Ke kaloku, kuphakanyiswa ukuba siqwalasele tabular nendlela kwesisombululo ilandelayo ngxaki.

NguDmitry, Anatoly kunye Lyudmila ke abalandeli imbalelwano yeposi, siyazi ukuba sonke bahlala kwiindawo ezahlukeneyo zehlabathi kwaye zokuzonwabisa ezahlukeneyo. Ukumisela abahlala yintoni isixeko noko abanomdla. Ezi zibakala zilandelayo:

• Dmitri akuzange eParis, kunye Lyudmila - eRoma;
• umntu ohlala e Paris, akufani movie;
• umntu ohlala eRome, iye uyakhala;
• Lyudmila Ukwehluleka ballet.

Ukuze bacombulule le ngxaki, kufuneka wenze itafile encinane.

France	Italy	United States		vocals	ballet	movie
			ngokuba nguDmitry
			Anatoly
			Lyudmila

Okulandelayo, kufuneka ingqalelo eliphezulu. Yonke ufunda kule imeko, kufuneka ziboniswe kule theyibhile. Ebudeni kokuzaliswa uya kuba acacileyo ngolu hlobo lulandelayo:

• NguDmitry uhlala eRoma yaye uyakhala;
• Anatoly uhlala eParis kwaye ivamile ballet;
• Lyudmila - fan enkulu cinema, ohlala eUnited States.

Nceda kwakhona ingqalelo yakhe ukuba ibinzana lokwenyaniso ziyaphawulwa inombolo 1 kunye lobuxoki - 0 Fakela etafileni le miqondiso, uya ufumane impendulo yombuzo osithandayo.

Mikroskhematika

Imizekelo ukuguquka amabinzana ubhalo ukuba esiye sakuphonononga, zibe kakhulu nzima xa efika kuqala. Amatikiti imeko yoviwo karhulumente enobunye unako zonke zinikwe ngohlobo neetshiphusi.

Kubalulekile ukwazi ukuba zonke izixhobo digital zisekelwe kwiziqalelo logic, oko kukuthi, ezinye izixhobo ukuba enze umsebenzi logic.

Sele sathetha ngayo umsebenzi onjalo njengokuba isihlanganisi (uphinda-phindo ubhalo). Oku kudla zibonakaliswe yi uphawu &. Lo msebenzi kuyimfuneko ukuba isihlanganisi imilinganiselo emininzi. Kulo mfanekiso uyakwazi ukubona wesekethe phindo enengqondo.

umsebenzi disjunction kuyimfuneko ukufezekisa disjunction kwezinye amaxabiso igalelo. Xa ubhala amagama lo msebenzi idla zibonakaliswe yi U isimboli. Kulo mfanekiso umzobo.

umsebenzi inversion i ibinzana converter enye kwenye. Kulo mfanekiso ungabona indlela isekethi ukhangela "hayi."

UMZEKELO lula olungumgubo №1

Le migaqo ingasentla lokuguqula amabinzana ubhalo kufuneka ikhuseleke practice. Kuya ekulandeleni le njongo, sicebisa ukuba ukusombulula ngokwabo imizekelo zabo ezimbini ubunzima medium of, kwaye xa kuthelekiswa neziphumo kweli candelo nqaku.

Ukuba andinalo ixesha lokuba ukhumbule formula yotshintsho amabinzana ubhalo, unako ukwenza i "isikhumbuzo" encinane. Uya kubona ukuba kungekudala uza kuhlola phezu kwakhe.

Umzekelo: (A + T) * (HEX + T) * (M + NO). Musa ungaveli ukubhala off, zama ukucombulula umzekelo ngokwakho.

Ebudeni zibe lula sifumana i kulandelayo entries: T * (M + akukho) = (T * M) + (T * No) = (T * NTU) + 0 = (T + 0) * (M + 0) = T * M.

Njengoko ubona kulo amazwi kunokuba ende nengenakusebenziseka ezintsonkothileyo, siye ndafumana elifutshane T * M. Ukuba nako ukusombulula kwi yabo kulo mzekelo, jonga kwakhona kwinqanaba apho wajonga inguqu amabinzana ubhalo, imisebenzi.

UMZEKELO lula olungumgubo №2

Kweli candelo, siza kukunika kuyacaciswa ibinzana (E + H) * (E + K). Makhe siqwalasele isicombululo ngokwamanqanaba. Into yokuqala ekufuneka ukuba uvule kwizibiyeli, khumbula ikhondo sokuqala lemathematika. Ngenxa yoko, nathi ufumane ibinzana zilandelayo: E + E * E * N * K * E * N + K. Ngaphezu koko, siphawula ukuba eli binzana yinxalenye E * E, khumbula idempotency umthetho nokuguqula yokungena: E + E * K * N * E * N + K. Inqanaba elilandelayo okuguqula le-E + E * Ngokusebenzisa bracketing le E-bume kunye nempahla: A + 1 = 1. Thina ukufumana athi zilandelayo: E + H + H * E * K. Emva indawo yokugqibela nelo kwaye uthathe kwizibiyeli E. Ngenxa yoko, sifumana impendulo: E + H * K.

Nikelani ingqalelo into yokuba lo msebenzi ibonakala kuphela nzima xa efika kuqala. Ukuze "flip kubo ezifana imbewu", kufuneka nje ukuba bafunde imithetho esisiseko ekuqiqeni.