{"id":1571,"date":"2024-11-14T02:34:37","date_gmt":"2024-11-13T19:34:37","guid":{"rendered":"https:\/\/www.tneutron.net\/industri\/?p=1571"},"modified":"2024-11-12T08:24:28","modified_gmt":"2024-11-12T01:24:28","slug":"boolean-algebra","status":"publish","type":"post","link":"https:\/\/www.tneutron.net\/industri\/boolean-algebra\/","title":{"rendered":"Boolean Algebra"},"content":{"rendered":"

Boolean algebra is algebra associated with binary variables and logic operations.<\/span> The variables are shown with letters of the alphabet, and three basic operations with AND, OR and NOT (complement).<\/span> Boolean function consists of binary variables that indicate the function, an equal sign, and an algebraic expression formed by using binary variables, constants 0 and 1, the symbols of logic operations, and parentheses.<\/span><\/p>\n

A Boolean function can be expressed in the truth table.<\/span> A truth table for a Boolean function is a list of all combinations of binary digits 0 and 1 are assigned to the binary variables and a list that shows the value of the function for each binary combination.<\/span> Boolean algebra has two distinct functions that are interconnected.<\/span> In a broad sense, boolean algebra means a kind of symbols invented by George Boole to manipulate the values of truth algebraic logic.<\/span><\/p>\n

In this case the boolean algebra suitable for application in the computer.<\/span> On the other hand, boolean algebra is also an algebraic structure whose operations meet certain rules.<\/span>
\n Dalil BOOLEAN;<\/strong><\/span>
\n 1. X = 0 OR X = 1<\/span>
\n 2. 0.<\/span> 0 = 0<\/span>
\n 3. 1 + 1 = 1<\/span>
\n 4. 0 + 0 = 0<\/span>
\n 5. 1.<\/span> 1 = 1<\/span>
\n 6. 1.<\/span> 0 = 0.<\/span> 1 = 0<\/span>
\n 7. 1 + 0 = 0 + 1 = 0<\/span><\/p>\n

THEOREM BOOLEAN<\/strong><\/span>
\n<\/strong> 1. HK.<\/span> commutative<\/span>
\n A + B = B + A<\/span>
\n A.<\/span> B = B.<\/span> A<\/span><\/p>\n

2. HK.<\/span> assosiative<\/span>
\n (A + B) + C = A + (B + C)<\/span>
\n (AB).<\/span> C = A.<\/span> (BC)<\/span><\/p>\n

3. HK.<\/span> Distributive<\/span>
\n A.<\/span> (B + C) = AB + AC<\/span>
\n A + (BC) = (A + B).<\/span> (A + C)<\/span><\/p>\n

4. HK.<\/span> negation<\/span>
\n (A “) = A”<\/span>
\n (A “)” = A<\/span><\/p>\n

5. HK.<\/span> ABRSORPSI<\/span>
\n A + AB = A<\/span>
\n A. (A + B) = A<\/span><\/p>\n

6. HK.<\/span> IDENTITY<\/span>
\n A + A = A<\/span>
\n A.<\/span> A = A<\/span><\/p>\n

7. DE MORGAN “S<\/span>
\n (A + B) ‘= A “.<\/span> B “<\/span>
\n (A, B) ‘= A “+ B”<\/span><\/p>\n

EXAMPLE:<\/strong><\/span>
\n<\/strong> 1. A + A.<\/span> B “+ A”.<\/span> B = A.<\/span> (1 + B “) + A”.<\/span> B<\/span>
\n = A.<\/span> 1 + A “.<\/span> B<\/span>
\n = A + A “.<\/span> B<\/span>
\n = A + B<\/span><\/p>\n

2. The series follows L<\/span>
\n\"image\"<\/a>
\n X = (AB) “.<\/span> B = (A “+ B”).<\/span> B<\/span>
\n = A “.B<\/span>
\n Or<\/span>
\n\"image\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Boolean algebra is algebra associated with binary variables and logic operations. The variables are shown with letters of the alphabet,<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","footnotes":""},"categories":[1830],"tags":[1947,1950,1956,1955,1953,1948,1951,1949,1954,1952],"class_list":["post-1571","post","type-post","status-publish","format-standard","hentry","category-english","tag-boolean-algebra","tag-boolean-algebra-calculator","tag-boolean-algebra-examples","tag-boolean-algebra-identities","tag-boolean-algebra-operators","tag-boolean-algebra-rules","tag-boolean-algebra-simplification","tag-boolean-algebra-simplifier","tag-boolean-algebra-symbols","tag-boolean-algebra-theorems"],"yoast_head":"\nBoolean Algebra - TN Industri<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.tneutron.net\/industri\/boolean-algebra\/\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"Boolean Algebra - TN Industri\" \/>\n<meta name=\"twitter:description\" content=\"Boolean algebra is algebra associated with binary variables and logic operations. 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