{"id":196854,"date":"2025-03-06T07:48:45","date_gmt":"2025-03-06T07:48:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196854"},"modified":"2025-03-06T07:48:48","modified_gmt":"2025-03-06T07:48:48","slug":"the-base-eleven-numeration-system-has-the-following-eleven-symbols","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/06\/the-base-eleven-numeration-system-has-the-following-eleven-symbols\/","title":{"rendered":"The base eleven numeration system has the following eleven symbols"},"content":{"rendered":"\n

The base eleven numeration system has the following eleven symbols: {0,1,2,3,4,5,6,7,8,9,A}, where A=10. Convert each of the following base 11 numerals into base ten numerals: 142 eleven = Aeieven ?= Aeleven ?= 1 Aeleven ?=<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To convert numbers from base 11 to base 10, we use positional notation, where each digit’s value depends on its position and the base’s power. In base 11, the digits are {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A}, with ‘A’ representing 10.\ue206<\/p>\n\n\n\n

Conversion Steps:<\/strong><\/p>\n\n\n\n

    \n
  1. Identify each digit and its position<\/strong>: Starting from the right (least significant digit), positions are indexed from 0 upwards.\ue206<\/li>\n\n\n\n
  2. Calculate each digit’s contribution<\/strong>: Multiply the digit by 11 raised to the power of its position index.\ue206<\/li>\n\n\n\n
  3. Sum all contributions<\/strong>: The total is the equivalent base 10 value.\ue206<\/li>\n<\/ol>\n\n\n\n

    Examples:<\/strong><\/p>\n\n\n\n

      \n
    1. 142\u2081\u2081<\/strong>:<\/li>\n<\/ol>\n\n\n\n
        \n
      • Digits: 1 (position 2), 4 (position 1), 2 (position 0)\ue206<\/li>\n\n\n\n
      • Calculations:\ue206\n
          \n
        • 1 \u00d7 11\u00b2 = 1 \u00d7 121 = 121<\/li>\n\n\n\n
        • 4 \u00d7 11\u00b9 = 4 \u00d7 11 = 44<\/li>\n\n\n\n
        • 2 \u00d7 11\u2070 = 2 \u00d7 1 = 2<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Sum: 121 + 44 + 2 = 167\ue206<\/li>\n\n\n\n
        • Result<\/strong>: 142\u2081\u2081 = 167\u2081\u2080\ue206<\/li>\n<\/ul>\n\n\n\n
            \n
          1. A1\u2081\u2081<\/strong>:<\/li>\n<\/ol>\n\n\n\n
              \n
            • Digits: A (position 1), 1 (position 0)\ue206<\/li>\n\n\n\n
            • Calculations:\ue206\n
                \n
              • A = 10<\/li>\n\n\n\n
              • 10 \u00d7 11\u00b9 = 10 \u00d7 11 = 110<\/li>\n\n\n\n
              • 1 \u00d7 11\u2070 = 1 \u00d7 1 = 1<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • Sum: 110 + 1 = 111\ue206<\/li>\n\n\n\n
              • Result<\/strong>: A1\u2081\u2081 = 111\u2081\u2080\ue206<\/li>\n<\/ul>\n\n\n\n
                  \n
                1. 1A1\u2081\u2081<\/strong>:<\/li>\n<\/ol>\n\n\n\n
                    \n
                  • Digits: 1 (position 2), A (position 1), 1 (position 0)\ue206<\/li>\n\n\n\n
                  • Calculations:\ue206\n
                      \n
                    • 1 \u00d7 11\u00b2 = 1 \u00d7 121 = 121<\/li>\n\n\n\n
                    • A = 10<\/li>\n\n\n\n
                    • 10 \u00d7 11\u00b9 = 10 \u00d7 11 = 110<\/li>\n\n\n\n
                    • 1 \u00d7 11\u2070 = 1 \u00d7 1 = 1<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                    • Sum: 121 + 110 + 1 = 232\ue206<\/li>\n\n\n\n
                    • Result<\/strong>: 1A1\u2081\u2081 = 232\u2081\u2080\ue206<\/li>\n<\/ul>\n\n\n\n

                      Explanation:<\/strong><\/p>\n\n\n\n

                      In positional notation, the value of a digit is determined by its face value multiplied by the base raised to the power of its position index. For base 11, each position represents a power of 11:\ue206<\/p>\n\n\n\n

                        \n
                      • Position 0: 11\u2070 = 1\ue206<\/li>\n\n\n\n
                      • Position 1: 11\u00b9 = 11\ue206<\/li>\n\n\n\n
                      • Position 2: 11\u00b2 = 121\ue206<\/li>\n\n\n\n
                      • And so on.\ue206<\/li>\n<\/ul>\n\n\n\n

                        By multiplying each digit by the corresponding power of 11 and summing the results, we obtain the number’s value in base 10.\ue206<\/p>\n","protected":false},"excerpt":{"rendered":"

                        The base eleven numeration system has the following eleven symbols: {0,1,2,3,4,5,6,7,8,9,A}, where A=10. Convert each of the following base 11 numerals into base ten numerals: 142 eleven = Aeieven ?= Aeleven ?= 1 Aeleven ?= The correct answer and explanation is : To convert numbers from base 11 to base 10, we use positional notation, […]<\/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-196854","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196854","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=196854"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196854\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196854"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196854"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196854"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}