{"id":93297,"date":"2025-06-01T11:46:51","date_gmt":"2025-06-01T11:46:51","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93297"},"modified":"2025-06-01T11:46:51","modified_gmt":"2025-06-01T11:46:51","slug":"the-result-of-binary-addition-of-8-and-2-in-twos-complement-form","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/","title":{"rendered":"The result of binary addition of \u2013 8 and \u2013 2 in two’s complement form"},"content":{"rendered":"

The result of binary addition of \u2013 8 and \u2013 2 in two’s complement form is :<\/p>\n

[amp_mcq option1=”10110″ option2=”0110″ option3=”1110″ option4=”0111″ correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nTo perform binary addition of -8 and -2 in two’s complement, we first need to represent these numbers in two’s complement form using a sufficient number of bits. Since the result -10 is needed, and the options suggest 4 or 5 bits, let’s use 5 bits as 4 bits is insufficient to represent -10 (-8 to +7 range for 4 bits).
\n<\/section>\n
\n– Convert positive 8 and 2 to binary (5 bits):
\n – 8 = 01000
\n – 2 = 00010
\n– Find two’s complement of 8 (for -8):
\n – Invert bits: 10111
\n – Add 1: 10111 + 1 = 11000 (This is -8 in 5-bit two’s complement)
\n– Find two’s complement of 2 (for -2):
\n – Invert bits: 11101
\n – Add 1: 11101 + 1 = 11110 (This is -2 in 5-bit two’s complement)
\n– Perform binary addition:
\n 11000 (-8)
\n+ 11110 (-2)
\n——-
\n 110110
\n– In 5-bit two’s complement addition, the carry-out from the most significant bit is discarded if the result is within the representable range. The result within 5 bits is 10110.
\n– To verify 10110, it is a negative number (starts with 1). Take two’s complement: Invert (01001), add 1 (01010). 01010 is 10 in decimal. Since it was negative, 10110 represents -10.
\n<\/section>\n
\nThe sum -8 + (-2) = -10. The 5-bit two’s complement representation of -10 is 10110, which matches option A. If we had used 4 bits, -8 is 1000, -2 is 1110. 1000 + 1110 = 10110. Truncating to 4 bits gives 0110, which is +6, an incorrect result due to overflow\/insufficient bits for the sum. Therefore, 5 bits is necessary and 10110 is the correct result in that format.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The result of binary addition of \u2013 8 and \u2013 2 in two’s complement form is : [amp_mcq option1=”10110″ option2=”0110″ option3=”1110″ option4=”0111″ correct=”option1″] This question was previously asked in UPSC CISF-AC-EXE – 2023 Download PDFAttempt Online To perform binary addition of -8 and -2 in two’s complement, we first need to represent these numbers in … <\/p>\n

Detailed SolutionThe result of binary addition of \u2013 8 and \u2013 2 in two’s complement form<\/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":[1105,1113],"class_list":["post-93297","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1105","tag-information-and-communication-technology","no-featured-image-padding"],"yoast_head":"\nThe result of binary addition of \u2013 8 and \u2013 2 in two's complement form<\/title>\n<meta name=\"description\" content=\"To perform binary addition of -8 and -2 in two's complement, we first need to represent these numbers in two's complement form using a sufficient number of bits. Since the result -10 is needed, and the options suggest 4 or 5 bits, let's use 5 bits as 4 bits is insufficient to represent -10 (-8 to +7 range for 4 bits). - Convert positive 8 and 2 to binary (5 bits): - 8 = 01000 - 2 = 00010 - Find two's complement of 8 (for -8): - Invert bits: 10111 - Add 1: 10111 + 1 = 11000 (This is -8 in 5-bit two's complement) - Find two's complement of 2 (for -2): - Invert bits: 11101 - Add 1: 11101 + 1 = 11110 (This is -2 in 5-bit two's complement) - Perform binary addition: 11000 (-8) + 11110 (-2) ------- 110110 - In 5-bit two's complement addition, the carry-out from the most significant bit is discarded if the result is within the representable range. The result within 5 bits is 10110. - To verify 10110, it is a negative number (starts with 1). Take two's complement: Invert (01001), add 1 (01010). 01010 is 10 in decimal. Since it was negative, 10110 represents -10.\" \/>\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\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The result of binary addition of \u2013 8 and \u2013 2 in two's complement form\" \/>\n<meta property=\"og:description\" content=\"To perform binary addition of -8 and -2 in two's complement, we first need to represent these numbers in two's complement form using a sufficient number of bits. Since the result -10 is needed, and the options suggest 4 or 5 bits, let's use 5 bits as 4 bits is insufficient to represent -10 (-8 to +7 range for 4 bits). - Convert positive 8 and 2 to binary (5 bits): - 8 = 01000 - 2 = 00010 - Find two's complement of 8 (for -8): - Invert bits: 10111 - Add 1: 10111 + 1 = 11000 (This is -8 in 5-bit two's complement) - Find two's complement of 2 (for -2): - Invert bits: 11101 - Add 1: 11101 + 1 = 11110 (This is -2 in 5-bit two's complement) - Perform binary addition: 11000 (-8) + 11110 (-2) ------- 110110 - In 5-bit two's complement addition, the carry-out from the most significant bit is discarded if the result is within the representable range. The result within 5 bits is 10110. - To verify 10110, it is a negative number (starts with 1). Take two's complement: Invert (01001), add 1 (01010). 01010 is 10 in decimal. Since it was negative, 10110 represents -10.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:46:51+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":"The result of binary addition of \u2013 8 and \u2013 2 in two's complement form","description":"To perform binary addition of -8 and -2 in two's complement, we first need to represent these numbers in two's complement form using a sufficient number of bits. Since the result -10 is needed, and the options suggest 4 or 5 bits, let's use 5 bits as 4 bits is insufficient to represent -10 (-8 to +7 range for 4 bits). - Convert positive 8 and 2 to binary (5 bits): - 8 = 01000 - 2 = 00010 - Find two's complement of 8 (for -8): - Invert bits: 10111 - Add 1: 10111 + 1 = 11000 (This is -8 in 5-bit two's complement) - Find two's complement of 2 (for -2): - Invert bits: 11101 - Add 1: 11101 + 1 = 11110 (This is -2 in 5-bit two's complement) - Perform binary addition: 11000 (-8) + 11110 (-2) ------- 110110 - In 5-bit two's complement addition, the carry-out from the most significant bit is discarded if the result is within the representable range. The result within 5 bits is 10110. - To verify 10110, it is a negative number (starts with 1). Take two's complement: Invert (01001), add 1 (01010). 01010 is 10 in decimal. Since it was negative, 10110 represents -10.","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\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/","og_locale":"en_US","og_type":"article","og_title":"The result of binary addition of \u2013 8 and \u2013 2 in two's complement form","og_description":"To perform binary addition of -8 and -2 in two's complement, we first need to represent these numbers in two's complement form using a sufficient number of bits. Since the result -10 is needed, and the options suggest 4 or 5 bits, let's use 5 bits as 4 bits is insufficient to represent -10 (-8 to +7 range for 4 bits). - Convert positive 8 and 2 to binary (5 bits): - 8 = 01000 - 2 = 00010 - Find two's complement of 8 (for -8): - Invert bits: 10111 - Add 1: 10111 + 1 = 11000 (This is -8 in 5-bit two's complement) - Find two's complement of 2 (for -2): - Invert bits: 11101 - Add 1: 11101 + 1 = 11110 (This is -2 in 5-bit two's complement) - Perform binary addition: 11000 (-8) + 11110 (-2) ------- 110110 - In 5-bit two's complement addition, the carry-out from the most significant bit is discarded if the result is within the representable range. The result within 5 bits is 10110. - To verify 10110, it is a negative number (starts with 1). Take two's complement: Invert (01001), add 1 (01010). 01010 is 10 in decimal. Since it was negative, 10110 represents -10.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:46:51+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\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/","name":"The result of binary addition of \u2013 8 and \u2013 2 in two's complement form","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:46:51+00:00","dateModified":"2025-06-01T11:46:51+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"To perform binary addition of -8 and -2 in two's complement, we first need to represent these numbers in two's complement form using a sufficient number of bits. Since the result -10 is needed, and the options suggest 4 or 5 bits, let's use 5 bits as 4 bits is insufficient to represent -10 (-8 to +7 range for 4 bits). - Convert positive 8 and 2 to binary (5 bits): - 8 = 01000 - 2 = 00010 - Find two's complement of 8 (for -8): - Invert bits: 10111 - Add 1: 10111 + 1 = 11000 (This is -8 in 5-bit two's complement) - Find two's complement of 2 (for -2): - Invert bits: 11101 - Add 1: 11101 + 1 = 11110 (This is -2 in 5-bit two's complement) - Perform binary addition: 11000 (-8) + 11110 (-2) ------- 110110 - In 5-bit two's complement addition, the carry-out from the most significant bit is discarded if the result is within the representable range. The result within 5 bits is 10110. - To verify 10110, it is a negative number (starts with 1). Take two's complement: Invert (01001), add 1 (01010). 01010 is 10 in decimal. Since it was negative, 10110 represents -10.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-result-of-binary-addition-of-8-and-2-in-twos-complement-form\/#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":"The result of binary addition of \u2013 8 and \u2013 2 in two’s complement form"}]},{"@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\/93297","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=93297"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/93297\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=93297"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=93297"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=93297"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}