Cov zajlus kom lub lag luam. Cov yooj yim logic hauj lwm

Khoos phib tawj science raws li ib tug science ntawm sau hom kev kawm, npaj thiab ua ib tug ntau yam ntawm cov ntaub ntawv pib mus rau tsim nyob rau hauv nruab nrab-thib nees nkaum caug xyoo. Txawm tias ib co historians ntseeg tau hais tias thaum pib ntawm lub tsim ntawm computer science twb pw nyob rau hauv lub xyoo pua 17th, nrog rau cov invention ntawm cov thawj cov neeg kho tshuab tshuab xam zauv, feem ntau nyob qib qub nrog cov muaj hnub nyoog ntawm ntau tshaj computer technology. Nyob rau hauv lub 40s ntawm lub xyoo pua 20th, nrog lub advent ntawm thawj computers, computer science tau txais ib tug tshiab impetus rau txoj kev loj hlob.

Cov kev kawm ntawm txoj kev tshawb no Informatics

Nws yog nrog lub advent ntawm thawj computers tau ua tsim nyog los tsim txoj kev tshiab ntawm systematization, muab xam thiab ua cov loj cov ntaub ntawv poob lawm, raws li tau zoo raws li nyob rau hauv txoj kev loj hlob ntawm algorithms uas yuav cia tas nrho tej zaum ntawm tshiab computers. Informatics tau txais tus txheej xwm ntawm ib qho kev ywj scientific kev qhuab qhia, thiab tsiv tawm ntawm lub dav hlau ntawm zauv kawm le caag nyob rau hauv feem ntau.

Tag nrho cov niaj hnub lub computer science yog raws li nyob rau hauv cov zajlus kom ua hauj lwm. Lawv yuav tsum tau hu ua lub qhov tseem ceeb. Nyob rau hauv lub cajmeem, computer systems lub tswvyim ntawm logic lag luam - nws yog ib tug nkaus, uas yog generated tom qab ua ib cov tswvyim tshiab los yog ib tug nqi tsim nyob rau hauv lub hauv paus ntawm uas twb muaj lawm tswv yim. Ib co ntawm tej yam ua tej zaum yuav txawv nyob ntawm seb lub processor caij rau txim tuag commands. Txawm li cas los, muaj ib co ua hauj lwm uas cov kev ua zoo tag nrho uas twb muaj lawm systems. Qhov no ua lag luam, uas ua hauj lwm nrog cov ntsiab lus tseem ceeb rau lawv tus kheej, xws li tsis kam muab, los yog cov neeg uas hloov cov quantitative characterization tswv yim - ntxiv, rho, khu, sib faib.

Operands ntawm cov zajlus kom ua hauj lwm

Txij li thaum lub algebra logic txhais tau tias ua hauj lwm rau paub daws teeb notions, ces raws li operands tag nrho cov zajlus kom ua hauj lwm yog cov generalized cov ntaub ntawv hom. Classical hais, ua hauj lwm nrog algebra nqe lus yog cov nqe lus, cuav los yog muaj tseeb. Lub electronics thiab programming rau cov hauj lwm cov lus yog siv Boolean variables yeej muaj tseeb thiab cuav los yog integer nqi ntawm 1 (tseeb) thiab 0 (cuav). Nyob rau ib tug ua ke ntawm cov qhov tseem ceeb, raws li zoo kawg li tej zaum nws yuav sound, cov ua hauj lwm yog khi tshaj txoj thiab loj-scale zog. Tag nrho cov kev pab cuam code uas yog tseg rau ib tug computer los yog cov ntaus ntawv dynamically translates rau hauv ib tug sib lawv liag ntawm sawv daws yuav thiab zeros - lub universal code uas yuav tsum tau ua los ntawm tej yam ua.

Hom ntawm cov zajlus kom ua hauj lwm

Raws li hais ua ntej lawm, nyob rau hauv lub classical Boolean algebra , muaj 2 hom kev khiav dej num. Lub ntsiab zajlus kom ua hauj lwm rau binary cov ntaub ntawv hom - yog tej yam ua rau cov nqe lus nws tus kheej (unary, los yog ib, lag luam). Qhov no kuj yog ua hauj lwm uas tsim tshiab cov nqe lus nyob rau hauv lub hauv paus ntawm uas twb muaj lawm qhov tseem ceeb (binary ua hauj lwm, los yog ntxaib). Qhov kev txiav txim ntawm cov zajlus kom ua hauj lwm yog tib yam li thaum ua tej haujlwm zauv ntawm sab laug mus rau sab xis, nyob rau hauv view ntawm lub nkhaus.

Qhov yooj yim thiab ib tug ntawm cov feem ntau zoo-paub cov zog ntawm Boolean logic muaj nuj nqi yog tsis kam muab. Qhov no yooj yim logic lag luam yog ib tug opposite nqi ntawm lub tswv yim operand. Nyob rau hauv electronics, qhov kev txiav txim yog zaum kuj hu ua ib tug inversion. Piv txwv li, yog tias koj invert lub taub Tawvv "qhov tseeb", qhov tshwm sim yog "cuav". Thiab vice versa - lub negation ntawm lub qhov tseem ceeb "cuav" yuav ua nyob rau hauv ib tug nqi ntawm "muaj tseeb". Qhov no zajlus kom lag luam programming yog feem ntau siv rau branching algorithms thiab kev siv ntawm cov "xaiv" ntawm ib tug tom ntej txheej commands rau lub hauv paus ntawm cov uas twb tau los yog hloov tej yam kev mob.

binary lag luam

Nyob rau hauv computer programming thiab siv ib tug tsawg set ntawm binary (binary) ua hauj lwm. Lawv tau txais lawv lub npe los ntawm lub Latin lus lis, lub ntsiab lus "ob", thiab yog cov zoo zog uas yuav coj ob tug cov tswv yim cov lus thiab rov qab ib tug tshwm sim nyob rau hauv ib tug tshiab tus nqi. Rau kev qhia txog ntawm tag nrho cov zog ntawm Boolean algebra siv qhov tseeb ntxhuav.

Yuav ua li cas lawv yuav tsum

Qhov no system yog ua rau ib qhov nqi ntawm cov tswv yim operands thiab piav tag nrho cov uas ua qhov tseem ceeb, uas muaj peev xwm rov qab mus rau ib tug predetermined logic lag luam ntawm hais tias muab tswv yim tsis.

Qhov tseem nquag siv zog nyob rau hauv lub computer thiab lub computer technology yog zajlus kom tas li ntawd (disjunction) thiab cov zajlus kom sib npaug (tau).

tau

Cov zajlus kom cov lag luam "THIAB" - yog ib tug muaj nuj nqi ntawm cov kev xaiv ntawm lub tsawg ntawm ob los yog n tswv yim operands. Nyob rau nkag mus rau qhov no muaj nuj nqi yuav muaj ob (binary muaj nuj nqi), peb qhov tseem ceeb (ternary), los yog ib tug xov tooj unlimited kev operands (n-ary lag luam). Thaum xam qhov tshwm sim ntawm cov kev ua nws yuav ua me tshaj ntawm tus nkag tswv yim tseem ceeb.

Analogue rau hauv dog dig algebra yog ib tug muaj nuj nqi ntawm kev ua lej khu. Yog li ntawd, cov tau lag luam yog feem ntau xa mus rau raws li ib tug zajlus kom sib npaug. Thaum lub kos npe rau ntawm cov nuj nqi cov ntaubntawv povthawj siv kev ua los yog sib npaug kos npe rau (taw tes) los yog ib tug ampersand. Yog hais tias peb ua qhov tseeb lub rooj rau no muaj nuj nqi, nws yuav tsum pom tias cov nuj nqi yog teem rau "muaj tseeb" los yog 1, tsuas yog nrog rau qhov tseeb ntawm tag nrho cov tswv yim operands. Yog hais tias tsawg kawg yog ib tug ntawm cov tswv yim tsis yog pes tsawg, los yog tus nqi "cuav", qhov tshwm sim ntawm cov nuj nqi kuj yuav "cuav".

Qhov no qhia analogy nrog xam ua lej khu: multiplication, thiab lwm cov uas poob lawm ntawm tus xov tooj rau 0 raws li ib tug tshwm sim yeej ib txwm rov 0. no logic lag luam yog commutative: qhov kev txiav txim nyob rau hauv uas nws tau txais tswv yim tsis yuav tsis cuam tshuam zaum kawg tshwm sim ntawm lub xam.

Lwm feature ntawm no muaj nuj nqi yog associativity, los yog associativity. Qhov no tej khoom vaj tse tso cai rau lub xam ntawm lub binary ib theem zuj zus ntawm kev ua hauj lwm tsis coj mus rau hauv tus account qhov kev txiav txim ntawm kev ntsuam xyuas. Yog li ntawd, rau 3 los yog ntau tshaj sib law liag zajlus kom sib npaug lag luam yog tsis tsim nyog los noj mus rau hauv tus account lub nkhaus. Nyob rau hauv lub cajmeem, qhov no muaj nuj nqi yog feem ntau siv los mus ua kom paub tseeb tias qhov kev commands tua xwb yog hais tias tus sau ua ib pawg ntawm tej yam tej yam kev mob.

disjunction

Cov zajlus kom cov lag luam "LOS SIS" - hauv daim ntawv ntawm ib tug Boolean muaj nuj nqi, uas yog zoo li tus algebraic ntxiv. Lwm yam lub npe rau no muaj nuj nqi - zajlus kom tas li ntawd, lub disjunction. Ib yam li ntawd, raws li cov zajlus kom sib npaug lag luam, disjunction tej zaum yuav binary (xam tus nqi raws li nyob rau hauv ob nqe lus), ternary los yog n-ary.

Qhov tseeb cov lus rau qhov no zajlus kom lag luam yog ib tug zoo ntawm lwm txoj rau lub tau. Cov zajlus kom cov lag luam "LOS SIS" laij qhov zoo tshaj plaws tshwm sim ntawm cov khoom sib ceg. Disjunction tau txais cov qhov tso zis nqi "cuav", los yog 0 tsuas yog thaum tag nrho cov tswv yim tsis tau txais nrog rau qhov tseem ceeb 0 ( "cuav"). Nyob rau hauv lwm yam ntaub ntawv cov zis yuav tsum tau ua los ntawm cov nqi "muaj tseeb", los yog 1. sau no muaj nuj nqi yog feem ntau siv zauv kos npe rau ntawm qhov sib ntxiv ( "Plus") los yog ob tug ntsug ib daim hlab. Qhov thib ob variant yog thoob plaws nyob rau hauv feem ntau programming lus thiab najnpawb vim hais tias nws tso cai rau koj kom meej meej cais cov zajlus kom lag luam ntawm lub xam.

Cov kev thaj chaw ntawm cov zajlus kom ua hauj lwm

Basic logic ua hauj lwm, seb nws yog unary, binary, ternary los yog lwm yam kev khiav dej num, yog kev kawm mus rau tej yam kev cai thiab thaj chaw uas piav qhia txog lawv tus cwj pwm. Ib tug xws li yuav tsum muaj zog muaj los ntawm saum toj no-piav logic zog yog commutative.

Qhov no feature kom lub permutation muaj nuj nqi yuav muab cov operand nqi tsis hloov. Tsis yog txhua txhua tus tswv muaj cov cuab yeej no. Tsis zoo li cov tau thiab disjunction uas siav commutativity yuav tsum tau, cov nuj nqi ntawm matrix npaug yog tsis tau, thiab lub rearrangement ntawm cov yam tseem ceeb nyob rau hauv lub lag luam no yuav entail lub txiaj ntsim ntawm qhov kev hloov, raws li zoo raws li exponentiation.

Ib tug ntxiv nam ntawm

Ib qho tseem ceeb feature, uas yog feem ntau siv nyob rau hauv electronics thiab circuitry, yog lub subordination ntawm officers ntawm cov zajlus kom ua hauj lwm De Morgan cai.

Cov kev cai khi officers ntawm logic hauj lwm siv cov zajlus kom negation muaj nuj nqi, uas yog siv los qhia ib zajlus kom ua hauj lwm siv rau lwm yam. Piv txwv li, ib tug tau negation muaj nuj nqi tej zaum yuav qhia los ntawm cov disjunction negations cais operands. Nrog rau cov kev cai cov zajlus kom cov lag luam "THIAB", "LOS SIS" thiab vzaimovyrazheny tau muab los siv muaj tsawg heev kho vajtse nqi. Qhov no feature yog tsis tshua muaj pab tau nyob rau hauv Circuit Court tsim, raws li nws tso cai rau koj mus cawm cov kev pab nyob rau hauv lub xam thiab tsim ntawm tej daim.