{"id":4543,"date":"2025-03-25T11:01:26","date_gmt":"2025-03-25T05:31:26","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=4543"},"modified":"2025-07-16T14:20:49","modified_gmt":"2025-07-16T08:50:49","slug":"adders-and-subtractors","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/boolean-algebra\/adders-and-subtractors","title":{"rendered":"ADDERS AND SUBTRACTORS"},"content":{"rendered":"<h2 style=\"text-align: justify;\">Half Adder<\/h2>\n<p style=\"text-align: justify;\">The half adder is an arithmetic circuit used to perform the addition of two single bits. The two input variables to the half adder designate the augend and addend bits and the output variables produce the sum and carry. Let A and B are the two input variables and sum (S) and carry (C) are the two output variables. Then,<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4544 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/03\/half-adder.jpg\" alt=\" Half Adder\" width=\"449\" height=\"215\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/half-adder.jpg 449w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/half-adder-300x144.jpg 300w\" sizes=\"auto, (max-width: 449px) 100vw, 449px\" \/><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_79_1 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.madeeasy.in\/study\/ee\/boolean-algebra\/adders-and-subtractors\/#Full-Adder\" >Full Adder<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.madeeasy.in\/study\/ee\/boolean-algebra\/adders-and-subtractors\/#Half-Subtractor\" >Half Subtractor<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.madeeasy.in\/study\/ee\/boolean-algebra\/adders-and-subtractors\/#Full-Subtractor\" >Full Subtractor<\/a><\/li><\/ul><\/nav><\/div>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Full-Adder\"><\/span>Full Adder<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">A full adder is a combinational circuit that performs the arithmetic sum of three input bits. It consists of three input variables designated by augend, addend and the input carry bit. The two output variables produce the SUM and CARRY. Let the two input variables are denoted by A and B, represent the two significant bits to be added. The third input Ci represents the carry from the previous lower significant position. The two outputs are sum (S) and carry (Ci + 1).<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4545 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/03\/full-adder.jpg\" alt=\" Full Adder\" width=\"630\" height=\"571\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/full-adder.jpg 630w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/full-adder-300x272.jpg 300w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Half-Subtractor\"><\/span>Half Subtractor<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">A half subtractor is a combinational circuit that subtracts one bit from the other and produces the difference. A half subtractor circuit with two input variables designated as A (minuend) and B (subtrahend); and output variables as Difference \u2018D\u2019 and Borrow \u2018b\u2019 is shown in the figure below.<br \/>\nHere, the operation A minus B is performed. The borrow output \u2018b\u2019 will be \u20181\u2019 whenever A &lt; B. If A &lt; B, then subtraction is done by borrowing 1 from next higher order bit.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-4546 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/03\/half-subtractor.jpg\" alt=\" Half Subtractor\" width=\"578\" height=\"107\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/half-subtractor.jpg 578w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/half-subtractor-300x56.jpg 300w\" sizes=\"auto, (max-width: 578px) 100vw, 578px\" \/><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Full-Subtractor\"><\/span>Full Subtractor<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">A full subtractor is a combinational circuit which performs subtraction involving three bits, namely minuend bit, subtrahend bit and the borrow from the previous stage. The three inputs are A(mineund), B(subtrahend) and bi(borrow from the previous stage) and two outputs D(difference) and bi + 1(borrow out) as shown in figure.<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4547 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/03\/full-subtractor.jpg\" alt=\"Full Subtractor\" width=\"651\" height=\"426\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/full-subtractor.jpg 651w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/03\/full-subtractor-300x196.jpg 300w\" sizes=\"auto, (max-width: 651px) 100vw, 651px\" \/><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ee\/boolean-algebra\/combinational-and-sequential-circuits\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ee\/boolean-algebra\/code-converters\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-boolean-algebra\" target=\"_blank\" rel=\"noopener\"><strong>What is Boolean algebra?<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Half Adder The half adder is an arithmetic circuit used to perform the addition of two single bits. The two<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1291,5],"tags":[1480,1483,1481,1427,1432,1335,1337,1482,1336,1441],"class_list":["post-4543","post","type-post","status-publish","format-standard","hentry","category-boolean-algebra","category-ee","tag-adders-and-subtractors","tag-arithmetic-circuits","tag-binary-arithmetic","tag-digital-circuits","tag-digital-electronics","tag-full-adder","tag-full-subtractor","tag-half-adder","tag-half-subtractor","tag-logic-design"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=4543"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/4543\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=4543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=4543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=4543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}