Problem 6: -17 + (-31)<\/strong><\/h3>\n\n\n\nBinary representation (8-bit):<\/strong>
-17 \u2192 11101111<\/code>
-31 \u2192 11100001<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\narduinoCopyEdit 11101111 \n+ 11100001 \n-----------\n1 11010000 (9 bits: discard overflow bit) \nResult: 11010000 \u2192 Two's complement of this gives 72 \u2192 Answer is -72 \n<\/code><\/pre>\n\n\n\n
\n\n\n\nProblem 7: 51 – 78<\/strong><\/h3>\n\n\n\nThis becomes 51 + (-78)<\/strong>
51 \u2192 00110011<\/code>
-78 \u2192 10110010<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\nmarkdownCopyEdit 00110011 \n+ 10110010 \n-----------\n 11100101 \u2192 Two's complement of this gives 27 \u2192 Answer is -27 \n<\/code><\/pre>\n\n\n\n
\n\n\n\nProblem 8: -19 + 35<\/strong><\/h3>\n\n\n\n-19 \u2192 11101101<\/code>
35 \u2192 00100011<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\nmarkdownCopyEdit 11101101 \n+ 00100011 \n-----------\n 00010000 \u2192 Result is positive \u2192 Decimal: 16 \n<\/code><\/pre>\n\n\n\n
\n\n\n\nProblem 9: -71 + (-31)<\/strong><\/h3>\n\n\n\n-71 \u2192 10111001<\/code>
-31 \u2192 11100001<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\nmarkdownCopyEdit 10111001 \n+ 11100001 \n-----------\n1 10011010 (discard overflow) \nResult: 10011010 \u2192 Two's complement of this is 102 \u2192 Answer is -102 \n<\/code><\/pre>\n\n\n\n
\n\n\n\nProblem 10: -120 + (-127)<\/strong><\/h3>\n\n\n\n-120 \u2192 10001000<\/code>
-127 \u2192 10000001<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\npgsqlCopyEdit 10001000 \n+ 10000001 \n-----------\n1 00001001 (discard overflow) \nResult: 00001001 \u2192 9 \u2192 **Incorrect!** This is overflow! \nCorrect result exceeds 8-bit signed range (\u2212128 to 127) \u2192 **Overflow occurs** \n<\/code><\/pre>\n\n\n\n
\n\n\n\nTextbook-Style Explanation <\/strong><\/h3>\n\n\n\nTwo’s complement arithmetic is the standard method for performing binary arithmetic with signed integers in digital systems. In two’s complement representation, positive numbers are represented in standard binary form, while negative numbers are represented by inverting all bits of the number\u2019s absolute binary value and adding one. For 8-bit systems, the representable range is from -128 to +127.<\/p>\n\n\n\n
To add two signed numbers using two’s complement, convert both numbers into their 8-bit binary representations. For negative numbers, compute their two’s complement form. This involves inverting the bits of the absolute binary value and adding 1. Then, simply add the binary numbers together. If the result produces a 9-bit number, the leftmost carry bit (the overflow bit) is discarded.<\/p>\n\n\n\n
The result is interpreted as follows: if the leftmost bit (most significant bit) is 0, the result is positive and can be read directly. If the leftmost bit is 1, the result is negative. To find the actual value, take the two’s complement of the result and add a negative sign.<\/p>\n\n\n\n
Overflow occurs when the result of an addition falls outside the valid range of the signed integer format (for 8 bits, this is \u2212128 to +127). When adding two negative numbers results in a positive binary output (or vice versa), overflow is indicated, and the result is unreliable.<\/p>\n\n\n\n
Two’s complement arithmetic allows subtraction to be performed as addition of a negative, such as computing 51 \u2212 78 by adding 51 + (\u221278). This simplifies circuit design and enables consistent processing of both positive and negative integers.<\/p>\n\n\n\n
Understanding two’s complement is essential for low-level programming, computer architecture, and digital systems design.<\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-353.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"Perform twos complement arithmetic for the followings. 6. -17 + (-31) 7. 51 – 78 8. -19 + 35 9. -71 + (-31) 10. -120 + (-127) The Correct Answer and Explanation is: Problem 6: -17 + (-31) Binary representation (8-bit):-17 \u2192 11101111-31 \u2192 11100001 Addition: arduinoCopyEdit 11101111 + 11100001 ———– 1 11010000 (9 bits: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-232839","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232839","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=232839"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232839\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232839"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232839"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
-17 \u2192
11101111<\/code>
-31 \u2192 11100001<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\narduinoCopyEdit 11101111 \n+ 11100001 \n-----------\n1 11010000 (9 bits: discard overflow bit) \nResult: 11010000 \u2192 Two's complement of this gives 72 \u2192 Answer is -72 \n<\/code><\/pre>\n\n\n\n
\n\n\n\nProblem 7: 51 – 78<\/strong><\/h3>\n\n\n\nThis becomes 51 + (-78)<\/strong>
51 \u2192 00110011<\/code>
-78 \u2192 10110010<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\nmarkdownCopyEdit 00110011 \n+ 10110010 \n-----------\n 11100101 \u2192 Two's complement of this gives 27 \u2192 Answer is -27 \n<\/code><\/pre>\n\n\n\n
\n\n\n\nProblem 8: -19 + 35<\/strong><\/h3>\n\n\n\n-19 \u2192 11101101<\/code>
35 \u2192 00100011<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\nmarkdownCopyEdit 11101101 \n+ 00100011 \n-----------\n 00010000 \u2192 Result is positive \u2192 Decimal: 16 \n<\/code><\/pre>\n\n\n\n
\n\n\n\nProblem 9: -71 + (-31)<\/strong><\/h3>\n\n\n\n-71 \u2192 10111001<\/code>
-31 \u2192 11100001<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\nmarkdownCopyEdit 10111001 \n+ 11100001 \n-----------\n1 10011010 (discard overflow) \nResult: 10011010 \u2192 Two's complement of this is 102 \u2192 Answer is -102 \n<\/code><\/pre>\n\n\n\n
\n\n\n\nProblem 10: -120 + (-127)<\/strong><\/h3>\n\n\n\n-120 \u2192 10001000<\/code>
-127 \u2192 10000001<\/code><\/p>\n\n\n\nAddition:<\/strong><\/p>\n\n\n\npgsqlCopyEdit 10001000 \n+ 10000001 \n-----------\n1 00001001 (discard overflow) \nResult: 00001001 \u2192 9 \u2192 **Incorrect!** This is overflow! \nCorrect result exceeds 8-bit signed range (\u2212128 to 127) \u2192 **Overflow occurs** \n<\/code><\/pre>\n\n\n\n
\n\n\n\nTextbook-Style Explanation <\/strong><\/h3>\n\n\n\nTwo’s complement arithmetic is the standard method for performing binary arithmetic with signed integers in digital systems. In two’s complement representation, positive numbers are represented in standard binary form, while negative numbers are represented by inverting all bits of the number\u2019s absolute binary value and adding one. For 8-bit systems, the representable range is from -128 to +127.<\/p>\n\n\n\n
To add two signed numbers using two’s complement, convert both numbers into their 8-bit binary representations. For negative numbers, compute their two’s complement form. This involves inverting the bits of the absolute binary value and adding 1. Then, simply add the binary numbers together. If the result produces a 9-bit number, the leftmost carry bit (the overflow bit) is discarded.<\/p>\n\n\n\n
The result is interpreted as follows: if the leftmost bit (most significant bit) is 0, the result is positive and can be read directly. If the leftmost bit is 1, the result is negative. To find the actual value, take the two’s complement of the result and add a negative sign.<\/p>\n\n\n\n
Overflow occurs when the result of an addition falls outside the valid range of the signed integer format (for 8 bits, this is \u2212128 to +127). When adding two negative numbers results in a positive binary output (or vice versa), overflow is indicated, and the result is unreliable.<\/p>\n\n\n\n
Two’s complement arithmetic allows subtraction to be performed as addition of a negative, such as computing 51 \u2212 78 by adding 51 + (\u221278). This simplifies circuit design and enables consistent processing of both positive and negative integers.<\/p>\n\n\n\n
Understanding two’s complement is essential for low-level programming, computer architecture, and digital systems design.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Perform twos complement arithmetic for the followings. 6. -17 + (-31) 7. 51 – 78 8. -19 + 35 9. -71 + (-31) 10. -120 + (-127) The Correct Answer and Explanation is: Problem 6: -17 + (-31) Binary representation (8-bit):-17 \u2192 11101111-31 \u2192 11100001 Addition: arduinoCopyEdit 11101111 + 11100001 ———– 1 11010000 (9 bits: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-232839","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232839","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=232839"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232839\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232839"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232839"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}