Boolean iwu

Modern kọmputa dabeere na "oge ochie" electronic kọmputa, na-adabere na ụfọdụ postulates dị ka ụkpụrụ ndị bụ isi nke ọrụ. Ha na-akpọ iwu nke algebra nke mgbagha. The mbụ dị otú ahụ aka ná ntị kọwawo (-bụghị dị ka zuru ezu dị ka na ya ugbu ụdị) site na Gris oge ochie ọkà mmụta Aristotle.

N'ịnọchite anya a dị iche iche alaka nke mgbakọ na mwepụ nke na-amụrụ propositional Calculus, algebra nke mgbagha nwere ọtụtụ ọma kwekọọ Nchoputa na nkwubi okwu.

Iji mma ịghọta isiokwu, nyochaa echiche na ihe ga-enyere na iso na-maara iwu nke algebra nke mgbagha.

Ikekwe isi okwu na-amụ ịdọ aka ná ntị - kwuru. Nke a na ụdị okwu a na-apụghị ịbụ ma ezi na ụgha. Ọ na-pụta ụwa naanị otu n'ime ndị a mara. N'ihi ya nweta dabere nabatara eziokwu uru 1 falsity - 0, a oku na-aga na nkwupụta onwe ya ụfọdụ Latin akwụkwọ ozi: A, B, C. Na ọzọ okwu, usoro A = 1 pụtara na uru A bụ eziokwu. Na okwu nwere ike ịbịa na ọtụtụ ụzọ dị iche iche. A tụlere ebe omume na i nwere ike igosi na ha. Rịba ama na-na iwu nke algebra nke mgbagha agaghị ekwe omume ịmụta n'amaghị iwu.

1. The disjunction nke okwu abụọ - n'ihi ọrụ "ma ọ bụ". Ọ nwere ike na-abụ ma ụgha ma ọ bụ eziokwu. Ọ na-eji ihe nnọchianya «v».

2. njikọ. The N'ihi nke dị otú ahụ mere na okwu abụọ, ga-enwe a ọhụrụ kwuru ọ bụ eziokwu ma ọ bụrụ na ma okwu bụ eziokwu mbụ. Jiri "na" ọrụ, ndị nnọchiteanya "*".

3. pụtara. Operation "ma ọ bụrụ na A, mgbe B". N'ihi bụ a na nkwupụta, ụgha naanị ma ọ bụrụ na A eziokwu na okwu ụgha B. ọdabara akara "->".

4. The narị afọ ise tupu. Operation «A ọ bụrụ na naanị ma ọ bụrụ na V mgbe." Nkwupụta a bụ eziokwu mgbe ma variables nwere otu ntule. Jiri akara "<->".

E nwekwara a na usoro nke arụmọrụ, yiri mmetuta, ma n'isiokwu a, ha agaghị na-atụle.

Ugbu a, ka anyị tụlee n'ụzọ zuru ezu na ihe ndị bụ isi na iwu nke algebra nke mgbagha:

1. The commutative na commutative kwuru na a mgbanwe n'usoro nke Logical arụmọrụ nke njikọ ma ọ bụ disjunction na n'ihi enweghị mmetụta.

2. associative ma ọ bụ associative. Dị ka iwu a, na variables na arụmọrụ nke njikọ na disjunction nwere ike grouped.

3. The nkesa ma ọ bụ nkesa. Ihe kachasi mkpa n'ime iwu ahụ bụ na otu variables na arụmarụ nwere ike e si na brackets, anaghị agbanwe Baịbụl.

4. The iwu nke de Morgan (inversion ma ọ bụ negation). The negation ọrụ bụ Ẹkot na disjunction of njikọ negation input variables. The negation nke disjunction, n'aka nke ya, bụ hà njikọ nke negation nke otu variables.

5. ugboro abụọ na-ezighị ezi. Negation nke a na nkwupụta ugboro abụọ na-apụta na mbụ kwuru, ugboro atọ - ya agugo.

6. Iwu idempotency dị ka ndị a maka ezi uche mgbakwunye: xvxvxvx = x; maka multiplication: x ^ x ^ x ^ = x.

7. The iwu nke na-abụghị atuaha ekwu, sị: okwu abụọ, ma ọ bụrụ na ha na-emegiderịta, n'otu oge eziokwu ike.

8. The iwu nke ekwe n'etiti. N'etiti abụọ na-emegiderịta okwu otu - bụ eziokwu mgbe nile, na ọzọ - ụgha, ọ dịghị atọ.

9. absorption iwu nwere ike e dere na ndị dị otú a ụzọ ezi uche mgbakwunye: XV (x ^ y) = x, maka multiplication: x ^ (xvy) = x.

10. The iwu bonding. Abụọ n'akụkụ conjunctions na-enwe ike arapara ọnụ, akpụ a njikọ nke ala ọkwá. Mgbe nke a bụ agbanwe na nke mbụ conjunctions glued kpamkpam. Ihe ezi uche mgbakwunye:

(X ^ y) v (-x ^ y) = y.

Anyị na-ewere naanị ihe ndị kasị iwu nke algebra nke mgbagha, nke n'ezie nwere ike ịbụ na ọtụtụ ndị ọzọ, dị ka na-abụkarị ihe ezi uche arụmarụ dị ogologo na ornate anya, nke nwere ike a ga-ebipụ site n'itinye a nọmba nke yiri iwu.

Dị ka a na-achị, n'ihi na mma nke na-agụta na ịmata ihe na-arụpụta na-eji pụrụ iche tebụl. All ẹdude iwu nke algebra nke mgbagha, na table nke nwere n'ozuzu Ọdịdị nke okporo rektangulu-ese ndị na-ekesa kwa agbanwe na a iche iche cell. The ukwuu akụkụ, mfe ọ bụ iji nagide ya, na-eji table.