{"id":42112,"date":"2025-06-28T13:31:37","date_gmt":"2025-06-28T13:31:37","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42112"},"modified":"2025-06-28T13:31:39","modified_gmt":"2025-06-28T13:31:39","slug":"decimal-to-binary-and-hex-conversion","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/decimal-to-binary-and-hex-conversion\/","title":{"rendered":"Decimal to binary and Hex Conversion"},"content":{"rendered":"\n

Decimal to binary and Hex Conversion: a. Convert the decimal number 115 into binary. b. Convert the decimal number 898 into hexadecimal.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

a. Convert Decimal 115 to Binary<\/h3>\n\n\n\n

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

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

    \n
  1. 115 \u00f7 2 = 57, remainder 1<\/li>\n\n\n\n
  2. 57 \u00f7 2 = 28, remainder 1<\/li>\n\n\n\n
  3. 28 \u00f7 2 = 14, remainder 0<\/li>\n\n\n\n
  4. 14 \u00f7 2 = 7, remainder 0<\/li>\n\n\n\n
  5. 7 \u00f7 2 = 3, remainder 1<\/li>\n\n\n\n
  6. 3 \u00f7 2 = 1, remainder 1<\/li>\n\n\n\n
  7. 1 \u00f7 2 = 0, remainder 1<\/li>\n<\/ol>\n\n\n\n

    Now, reading the remainders from bottom to top: 115 in binary is 1110011<\/strong>.<\/p>\n\n\n\n

    b. Convert Decimal 898 to Hexadecimal<\/h3>\n\n\n\n

    For hexadecimal conversion, we divide the decimal number by 16, noting the remainder each time. The remainders correspond to hexadecimal digits: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15).<\/p>\n\n\n\n

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

      \n
    1. 898 \u00f7 16 = 56, remainder 2 (2 in hex)<\/li>\n\n\n\n
    2. 56 \u00f7 16 = 3, remainder 8 (8 in hex)<\/li>\n\n\n\n
    3. 3 \u00f7 16 = 0, remainder 3 (3 in hex)<\/li>\n<\/ol>\n\n\n\n

      Now, reading the remainders from bottom to top: 898 in hexadecimal is 382<\/strong>.<\/p>\n\n\n\n

      Explanation<\/h3>\n\n\n\n
        \n
      1. Binary Conversion (115)<\/strong>: Each division by 2 breaks down the number by halving it and tracking the remainder, which gives us the individual binary digits (bits). Since binary is a base-2 system, each remainder is either 0 or 1, and the remainders form the binary representation when read in reverse order.<\/li>\n\n\n\n
      2. Hexadecimal Conversion (898)<\/strong>: Hexadecimal is a base-16 number system, which is a more compact way to represent binary numbers. By dividing by 16, we group the binary digits in 4-bit chunks, as one hexadecimal digit can represent four binary digits. The remainder after each division tells us the value of the hexadecimal digit.<\/li>\n<\/ol>\n\n\n\n

        In both cases, the processes are similar but differ in the base used (2 for binary, 16 for hexadecimal). The goal is to break the decimal number into smaller, easier-to-read chunks in their respective bases.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Decimal to binary and Hex Conversion: a. Convert the decimal number 115 into binary. b. Convert the decimal number 898 into hexadecimal. The Correct Answer and Explanation is: a. Convert Decimal 115 to Binary To convert a decimal number to binary, we repeatedly divide the number by 2, recording the remainder at each step, and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-42112","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42112","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=42112"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42112\/revisions"}],"predecessor-version":[{"id":42114,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42112\/revisions\/42114"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}