{"id":218726,"date":"2025-05-24T10:52:38","date_gmt":"2025-05-24T10:52:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218726"},"modified":"2025-05-24T10:52:41","modified_gmt":"2025-05-24T10:52:41","slug":"the-octal-number-73-is-equivalent-to-the-decimal-number","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/24\/the-octal-number-73-is-equivalent-to-the-decimal-number\/","title":{"rendered":"The octal number 73 is equivalent to the decimal number"},"content":{"rendered":"\n<p>The octal number 73 is equivalent to the decimal number:<\/p>\n\n\n\n<p>(a) 47<br>(b) 59<br>(c) 111<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: (b) 59<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<p>To convert an octal number to its decimal equivalent, you must understand the base system involved. <strong>Octal<\/strong> is a base-8 number system, meaning each digit can range from 0 to 7. In contrast, <strong>decimal<\/strong> is a base-10 number system, the standard system we use every day.<\/p>\n\n\n\n<p>Let\u2019s convert the <strong>octal number 73<\/strong> to decimal:<\/p>\n\n\n\n<p>The octal number &#8220;73&#8221; consists of two digits:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The leftmost digit is 7 (which is in the 8\u00b9 position)<\/li>\n\n\n\n<li>The rightmost digit is 3 (which is in the 8\u2070 position)<\/li>\n<\/ul>\n\n\n\n<p>To convert to decimal, multiply each digit by 8 raised to the power of its position (starting from the right with position 0), and then sum the results:<\/p>\n\n\n\n<p>$$<br>\\text{Decimal equivalent} = (7 \\times 8^1) + (3 \\times 8^0)<br>$$<\/p>\n\n\n\n<p>$$<br>= (7 \\times 8) + (3 \\times 1)<br>$$<\/p>\n\n\n\n<p>$$<br>= 56 + 3 = \\boxed{59}<br>$$<\/p>\n\n\n\n<p>So, the octal number 73 is equal to the decimal number <strong>59<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Why This Works<\/strong><\/h3>\n\n\n\n<p>Each position in an octal number represents a power of 8, just as each position in a decimal number represents a power of 10. For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In decimal: 53 = (5 \u00d7 10\u00b9) + (3 \u00d7 10\u2070) = 50 + 3 = 53<\/li>\n\n\n\n<li>In octal: 73 = (7 \u00d7 8\u00b9) + (3 \u00d7 8\u2070) = 56 + 3 = 59<\/li>\n<\/ul>\n\n\n\n<p>This positional value system applies to all number bases.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion<\/strong><\/h3>\n\n\n\n<p>Option <strong>(b) 59<\/strong> is the correct answer. The conversion of base-8 (octal) to base-10 (decimal) involves multiplying each digit by powers of 8 and summing the results. Understanding base conversions is critical in computer science and digital electronics, where different base systems like binary, octal, and hexadecimal are frequently used.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/05\/image-326.png\" alt=\"\" class=\"wp-image-218727\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The octal number 73 is equivalent to the decimal number: (a) 47(b) 59(c) 111 The Correct Answer and Explanation is: Correct Answer: (b) 59 To convert an octal number to its decimal equivalent, you must understand the base system involved. Octal is a base-8 number system, meaning each digit can range from 0 to 7. [&hellip;]<\/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-218726","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218726","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=218726"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218726\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}