{"id":211388,"date":"2025-05-03T20:20:02","date_gmt":"2025-05-03T20:20:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=211388"},"modified":"2025-05-03T20:20:04","modified_gmt":"2025-05-03T20:20:04","slug":"decimal-to-binary-and-hex-conversion","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/03\/decimal-to-binary-and-hex-conversion\/","title":{"rendered":"Decimal to binary and Hex Conversion"},"content":{"rendered":"\n

Decimal to binary and Hex Conversion:<\/p>\n\n\n\n

Convert the decimal number 115 into binary.
Convert the decimal number 898 into hexadecimal.<\/p>\n\n\n\n

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

Let’s break down the process of converting the decimal numbers to binary and hexadecimal:<\/p>\n\n\n\n

1. Converting the decimal number 115 to binary:<\/strong><\/h3>\n\n\n\n

To convert a decimal number to binary, we repeatedly divide the number by 2, recording the remainders at each step. The binary number is the sequence of remainders, read from bottom to top.<\/p>\n\n\n\n

Let’s convert 115 into binary:<\/p>\n\n\n\n

    \n
  • 115 \u00f7 2 = 57, remainder = 1<\/li>\n\n\n\n
  • 57 \u00f7 2 = 28, remainder = 1<\/li>\n\n\n\n
  • 28 \u00f7 2 = 14, remainder = 0<\/li>\n\n\n\n
  • 14 \u00f7 2 = 7, remainder = 0<\/li>\n\n\n\n
  • 7 \u00f7 2 = 3, remainder = 1<\/li>\n\n\n\n
  • 3 \u00f7 2 = 1, remainder = 1<\/li>\n\n\n\n
  • 1 \u00f7 2 = 0, remainder = 1<\/li>\n<\/ul>\n\n\n\n

    Now, reading the remainders from bottom to top, we get: 1110011<\/strong>.<\/p>\n\n\n\n

    So, the binary equivalent of 115 is 1110011<\/strong>.<\/p>\n\n\n\n

    2. Converting the decimal number 898 to hexadecimal:<\/strong><\/h3>\n\n\n\n

    To convert a decimal number to hexadecimal, we repeatedly divide the number by 16, recording the remainders. The hexadecimal system uses digits 0-9 and letters A-F to represent values 0-15.<\/p>\n\n\n\n

    Let\u2019s convert 898 into hexadecimal:<\/p>\n\n\n\n

      \n
    • 898 \u00f7 16 = 56, remainder = 2<\/li>\n\n\n\n
    • 56 \u00f7 16 = 3, remainder = 8<\/li>\n\n\n\n
    • 3 \u00f7 16 = 0, remainder = 3<\/li>\n<\/ul>\n\n\n\n

      Now, reading the remainders from bottom to top, we get 382<\/strong>.<\/p>\n\n\n\n

      So, the hexadecimal equivalent of 898 is 382<\/strong>.<\/p>\n\n\n\n

      Explanation:<\/h3>\n\n\n\n
        \n
      • Binary system<\/strong> is a base-2 system, which means it only uses two digits: 0 and 1. Each binary digit (bit) represents a power of 2. For example, the binary number 1110011 is calculated as: $$
        1 \\times 2^6 + 1 \\times 2^5 + 1 \\times 2^4 + 0 \\times 2^3 + 0 \\times 2^2 + 1 \\times 2^1 + 1 \\times 2^0 = 115
        $$ The process of dividing by 2 repeatedly helps to break down the number into its binary representation.<\/li>\n\n\n\n
      • Hexadecimal system<\/strong> is a base-16 system, which means it uses digits 0-9 and letters A-F to represent values 0-15. It is commonly used in computing as a more compact way to represent binary numbers. In the example of 898, we divide by 16 because 16 is the base of the system. Each remainder corresponds to a hexadecimal digit, either a number or a letter.<\/li>\n<\/ul>\n\n\n\n

        In conclusion, understanding the processes of division and remainders allows us to convert decimal numbers to binary and hexadecimal systems effectively, which are commonly used in computing and digital electronics.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Decimal to binary and Hex Conversion: Convert the decimal number 115 into binary.Convert the decimal number 898 into hexadecimal. The correct answer and explanation is : Let’s break down the process of converting the decimal numbers to binary and hexadecimal: 1. Converting the decimal number 115 to binary: To convert a decimal number to binary, […]<\/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-211388","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211388","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=211388"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211388\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211388"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211388"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}