{"id":92907,"date":"2025-06-01T11:35:06","date_gmt":"2025-06-01T11:35:06","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92907"},"modified":"2025-06-01T11:35:06","modified_gmt":"2025-06-01T11:35:06","slug":"exclusive-or-binary-operation-can-be-represented-as","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/","title":{"rendered":"Exclusive-OR binary operation can be represented as"},"content":{"rendered":"

Exclusive-OR binary operation can be represented as<\/p>\n

[amp_mcq option1=”$\\bar{A} \\cdot B + A \\cdot \\bar{B}$” option2=”$A \\cdot \\bar{B} + \\bar{A} \\cdot B$” option3=”$A \\cdot B + \\bar{A} \\cdot \\bar{B}$” option4=”$(\\bar{A} + \\bar{B}) \\cdot (A + B)$” correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2020<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe Exclusive-OR (XOR) binary operation of two inputs A and B is true (1) if and only if the inputs are different. Its truth table is:
\nA | B | A XOR B
\n–|—|——–
\n0 | 0 | 0
\n0 | 1 | 1
\n1 | 0 | 1
\n1 | 1 | 0
\nThe Sum of Products (SOP) representation for this function includes minterms where the output is 1. These are when (A=0 and B=1) or (A=1 and B=0).
\n– A=0 and B=1 is represented as $\\bar{A} \\cdot B$.
\n– A=1 and B=0 is represented as $A \\cdot \\bar{B}$.
\nCombining these with an OR operator gives the SOP form: $\\bar{A} \\cdot B + A \\cdot \\bar{B}$.
\nOption A is $\\bar{A} \\cdot B + A \\cdot \\bar{B}$, which directly matches the standard SOP form of XOR.
\n<\/section>\n
\n– XOR outputs 1 when inputs are different.
\n– The standard SOP form of XOR(A, B) is $\\bar{A}B + A\\bar{B}$.
\n– Boolean algebra allows representing logic functions using AND (`.`), OR (`+`), and NOT (`bar` or prime).
\n<\/section>\n
\nOption B is identical to A due to the commutativity of addition. Option C represents XNOR ($A \\cdot B + \\bar{A} \\cdot \\bar{B}$), which is the complement of XOR. Option D, $(A+B)(\\bar{A}+\\bar{B})$, is the Product of Sums (POS) canonical form for XOR, also a correct representation. However, option A is the standard SOP form.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Exclusive-OR binary operation can be represented as [amp_mcq option1=”$\\bar{A} \\cdot B + A \\cdot \\bar{B}$” option2=”$A \\cdot \\bar{B} + \\bar{A} \\cdot B$” option3=”$A \\cdot B + \\bar{A} \\cdot \\bar{B}$” option4=”$(\\bar{A} + \\bar{B}) \\cdot (A + B)$” correct=”option1″] This question was previously asked in UPSC CISF-AC-EXE – 2020 Download PDFAttempt Online The Exclusive-OR (XOR) binary operation … <\/p>\n

Detailed SolutionExclusive-OR binary operation can be represented as<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1089],"tags":[1288,1113],"class_list":["post-92907","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1288","tag-information-and-communication-technology","no-featured-image-padding"],"yoast_head":"\nExclusive-OR binary operation can be represented as<\/title>\n<meta name=\"description\" content=\"The Exclusive-OR (XOR) binary operation of two inputs A and B is true (1) if and only if the inputs are different. Its truth table is: A | B | A XOR B --|---|-------- 0 | 0 | 0 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0 The Sum of Products (SOP) representation for this function includes minterms where the output is 1. These are when (A=0 and B=1) or (A=1 and B=0). - A=0 and B=1 is represented as $bar{A} cdot B$. - A=1 and B=0 is represented as $A cdot bar{B}$. Combining these with an OR operator gives the SOP form: $bar{A} cdot B + A cdot bar{B}$. Option A is $bar{A} cdot B + A cdot bar{B}$, which directly matches the standard SOP form of XOR. - XOR outputs 1 when inputs are different. - The standard SOP form of XOR(A, B) is $bar{A}B + Abar{B}$. - Boolean algebra allows representing logic functions using AND (`.`), OR (`+`), and NOT (`bar` or prime).\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Exclusive-OR binary operation can be represented as\" \/>\n<meta property=\"og:description\" content=\"The Exclusive-OR (XOR) binary operation of two inputs A and B is true (1) if and only if the inputs are different. Its truth table is: A | B | A XOR B --|---|-------- 0 | 0 | 0 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0 The Sum of Products (SOP) representation for this function includes minterms where the output is 1. These are when (A=0 and B=1) or (A=1 and B=0). - A=0 and B=1 is represented as $bar{A} cdot B$. - A=1 and B=0 is represented as $A cdot bar{B}$. Combining these with an OR operator gives the SOP form: $bar{A} cdot B + A cdot bar{B}$. Option A is $bar{A} cdot B + A cdot bar{B}$, which directly matches the standard SOP form of XOR. - XOR outputs 1 when inputs are different. - The standard SOP form of XOR(A, B) is $bar{A}B + Abar{B}$. - Boolean algebra allows representing logic functions using AND (`.`), OR (`+`), and NOT (`bar` or prime).\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:35:06+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Exclusive-OR binary operation can be represented as","description":"The Exclusive-OR (XOR) binary operation of two inputs A and B is true (1) if and only if the inputs are different. Its truth table is: A | B | A XOR B --|---|-------- 0 | 0 | 0 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0 The Sum of Products (SOP) representation for this function includes minterms where the output is 1. These are when (A=0 and B=1) or (A=1 and B=0). - A=0 and B=1 is represented as $bar{A} cdot B$. - A=1 and B=0 is represented as $A cdot bar{B}$. Combining these with an OR operator gives the SOP form: $bar{A} cdot B + A cdot bar{B}$. Option A is $bar{A} cdot B + A cdot bar{B}$, which directly matches the standard SOP form of XOR. - XOR outputs 1 when inputs are different. - The standard SOP form of XOR(A, B) is $bar{A}B + Abar{B}$. - Boolean algebra allows representing logic functions using AND (`.`), OR (`+`), and NOT (`bar` or prime).","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/","og_locale":"en_US","og_type":"article","og_title":"Exclusive-OR binary operation can be represented as","og_description":"The Exclusive-OR (XOR) binary operation of two inputs A and B is true (1) if and only if the inputs are different. Its truth table is: A | B | A XOR B --|---|-------- 0 | 0 | 0 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0 The Sum of Products (SOP) representation for this function includes minterms where the output is 1. These are when (A=0 and B=1) or (A=1 and B=0). - A=0 and B=1 is represented as $bar{A} cdot B$. - A=1 and B=0 is represented as $A cdot bar{B}$. Combining these with an OR operator gives the SOP form: $bar{A} cdot B + A cdot bar{B}$. Option A is $bar{A} cdot B + A cdot bar{B}$, which directly matches the standard SOP form of XOR. - XOR outputs 1 when inputs are different. - The standard SOP form of XOR(A, B) is $bar{A}B + Abar{B}$. - Boolean algebra allows representing logic functions using AND (`.`), OR (`+`), and NOT (`bar` or prime).","og_url":"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:35:06+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/","url":"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/","name":"Exclusive-OR binary operation can be represented as","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:35:06+00:00","dateModified":"2025-06-01T11:35:06+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The Exclusive-OR (XOR) binary operation of two inputs A and B is true (1) if and only if the inputs are different. Its truth table is: A | B | A XOR B --|---|-------- 0 | 0 | 0 0 | 1 | 1 1 | 0 | 1 1 | 1 | 0 The Sum of Products (SOP) representation for this function includes minterms where the output is 1. These are when (A=0 and B=1) or (A=1 and B=0). - A=0 and B=1 is represented as $\\bar{A} \\cdot B$. - A=1 and B=0 is represented as $A \\cdot \\bar{B}$. Combining these with an OR operator gives the SOP form: $\\bar{A} \\cdot B + A \\cdot \\bar{B}$. Option A is $\\bar{A} \\cdot B + A \\cdot \\bar{B}$, which directly matches the standard SOP form of XOR. - XOR outputs 1 when inputs are different. - The standard SOP form of XOR(A, B) is $\\bar{A}B + A\\bar{B}$. - Boolean algebra allows representing logic functions using AND (`.`), OR (`+`), and NOT (`bar` or prime).","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/exclusive-or-binary-operation-can-be-represented-as\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CISF-AC-EXE","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cisf-ac-exe\/"},{"@type":"ListItem","position":3,"name":"Exclusive-OR binary operation can be represented as"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92907","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=92907"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92907\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=92907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=92907"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=92907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}