{"id":996,"date":"2026-04-07T22:01:02","date_gmt":"2026-04-07T16:16:02","guid":{"rendered":"https:\/\/rijankc.com.np\/?p=996"},"modified":"2026-04-07T22:01:02","modified_gmt":"2026-04-07T16:16:02","slug":"binary-number-system-to-decimal-octal-and-hexadecimal-conversion","status":"publish","type":"post","link":"https:\/\/rijankc.com.np\/?p=996","title":{"rendered":"Binary Number System to Decimal, Octal and Hexadecimal Conversion"},"content":{"rendered":"

Below is a step-by-step tutorial<\/strong> showing how to convert a binary number into Decimal, Octal, and Hexadecimal <\/strong>Number system.<\/p>\n

\n

Example Binary Number<\/h1>\n

Let\u2019s use:<\/p>\n

Binary = 101101.101\u2082<\/strong><\/p>\n

This number has:<\/p>\n

    \n
  • Integer part \u2192 101101<\/code><\/li>\n
  • Fraction part \u2192 .101<\/code><\/li>\n<\/ul>\n
    \n

    1) Binary \u279c Decimal Conversion<\/h1>\n

    Rule<\/h3>\n

    Each binary digit represents a power of 2.<\/p>\n

    Positions left of decimal:
    \u2026 2\u2075 2\u2074 2\u00b3 2\u00b2 2\u00b9 2\u2070<\/p>\n

    Positions right of decimal:
    2\u207b\u00b9 2\u207b\u00b2 2\u207b\u00b3 \u2026<\/p>\n

    \n

    Step 1: Convert Integer Part (101101\u2082)<\/h2>\n

    Write powers of 2 under each digit:<\/p>\n

    \n
    \n\n\n\n\n\n
    Binary<\/th>\n1<\/th>\n0<\/th>\n1<\/th>\n1<\/th>\n0<\/th>\n1<\/th>\n<\/tr>\n<\/thead>\n
    Power<\/td>\n2\u2075<\/td>\n2\u2074<\/td>\n2\u00b3<\/td>\n2\u00b2<\/td>\n2\u00b9<\/td>\n2\u2070<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

    Now multiply and add:<\/p>\n

    = 1\u00d72\u2075 + 0\u00d72\u2074 + 1\u00d72\u00b3 + 1\u00d72\u00b2 + 0\u00d72\u00b9 + 1\u00d72\u2070
    = 1\u00d732 + 0\u00d716 + 1\u00d78 + 1\u00d74 + 0\u00d72 + 1\u00d71
    = 32 + 0 + 8 + 4 + 0 + 1
    = 45<\/strong><\/p>\n

    \n

    Step 2: Convert Fraction Part (.101\u2082)<\/h2>\n
    \n
    \n\n\n\n\n\n
    Binary<\/th>\n1<\/th>\n0<\/th>\n1<\/th>\n<\/tr>\n<\/thead>\n
    Power<\/td>\n2\u207b\u00b9<\/td>\n2\u207b\u00b2<\/td>\n2\u207b\u00b3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

    = 1\u00d7\u00bd + 0\u00d7\u00bc + 1\u00d7\u215b
    = 0.5 + 0 + 0.125
    = 0.625<\/strong><\/p>\n

    \n

    Final Decimal Answer<\/h3>\n

    101101.101\u2082 = 45.625\u2081\u2080<\/strong><\/p>\n

    \n

    2) Binary \u279c Octal Conversion<\/h1>\n

    Rule<\/h3>\n

    Group binary digits in sets of 3 bits<\/strong> from the decimal point.<\/p>\n

    \n

    Step 1: Group Integer Part<\/h2>\n

    Binary: 101101
    Group into 3 bits from right:<\/p>\n

    101 101<\/p>\n

    Convert each group to decimal:<\/p>\n

    \n
    \n\n\n\n\n\n\n
    Binary<\/th>\nDecimal<\/th>\n<\/tr>\n<\/thead>\n
    101<\/td>\n5<\/td>\n<\/tr>\n
    101<\/td>\n5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

    Integer part \u2192 55\u2088<\/strong><\/p>\n

    \n

    Step 2: Group Fraction Part<\/h2>\n

    Fraction: .101
    Group from left:<\/p>\n

    101<\/p>\n

    \n
    \n\n\n\n\n\n
    Binary<\/th>\nDecimal<\/th>\n<\/tr>\n<\/thead>\n
    101<\/td>\n5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

    Fraction part \u2192 .5\u2088<\/strong><\/p>\n

    \n

    Final Octal Answer<\/h3>\n

    101101.101\u2082 = 55.5\u2088<\/strong><\/p>\n

    \n

    3) Binary \u279c Hexadecimal Conversion<\/h1>\n

    Rule<\/h3>\n

    Group binary digits in sets of 4 bits<\/strong>.<\/p>\n

    \n

    Step 1: Group Integer Part<\/h2>\n

    Binary: 101101
    Add leading zeros to make groups of 4:<\/p>\n

    0010 1101<\/p>\n

    Convert each group:<\/p>\n

    \n
    \n\n\n\n\n\n\n
    Binary<\/th>\nDecimal<\/th>\nHex<\/th>\n<\/tr>\n<\/thead>\n
    0010<\/td>\n2<\/td>\n2<\/td>\n<\/tr>\n
    1101<\/td>\n13<\/td>\nD<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

    Integer part \u2192 2D<\/strong><\/p>\n

    \n

    Step 2: Group Fraction Part<\/h2>\n

    Fraction: .101
    Add trailing zeros:<\/p>\n

    .1010<\/p>\n

    \n
    \n\n\n\n\n\n
    Binary<\/th>\nDecimal<\/th>\nHex<\/th>\n<\/tr>\n<\/thead>\n
    1010<\/td>\n10<\/td>\nA<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n

    Fraction part \u2192 .A<\/strong><\/p>\n

    \n

    Final Hexadecimal Answer<\/h3>\n

    101101.101\u2082 = 2D.A\u2081\u2086<\/strong><\/p>\n

    \n

    Final Summary Table<\/h1>\n
    \n
    \n\n\n\n\n\n\n\n
    Conversion<\/th>\nResult<\/th>\n<\/tr>\n<\/thead>\n
    Decimal<\/td>\n45.625\u2081\u2080<\/strong><\/td>\n<\/tr>\n
    Octal<\/td>\n55.5\u2088<\/strong><\/td>\n<\/tr>\n
    Hexadecimal<\/td>\n2D.A\u2081\u2086<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    Below is a step-by-step tutorial showing how to convert a binary number into Decimal, Octal, and Hexadecimal Number system. Example Binary Number Let\u2019s use: Binary = 101101.101\u2082 This number has: Integer part \u2192 101101 Fraction part \u2192 .101 1) Binary \u279c Decimal Conversion Rule Each binary digit represents a power of 2. Positions left of […]<\/p>\n","protected":false},"author":1,"featured_media":997,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"footnotes":""},"categories":[147,145,146],"tags":[],"class_list":["post-996","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-binary-number-system","category-computer-science","category-number-system"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/rijankc.com.np\/index.php?rest_route=\/wp\/v2\/posts\/996","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rijankc.com.np\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rijankc.com.np\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rijankc.com.np\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/rijankc.com.np\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=996"}],"version-history":[{"count":1,"href":"https:\/\/rijankc.com.np\/index.php?rest_route=\/wp\/v2\/posts\/996\/revisions"}],"predecessor-version":[{"id":998,"href":"https:\/\/rijankc.com.np\/index.php?rest_route=\/wp\/v2\/posts\/996\/revisions\/998"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rijankc.com.np\/index.php?rest_route=\/wp\/v2\/media\/997"}],"wp:attachment":[{"href":"https:\/\/rijankc.com.np\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rijankc.com.np\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rijankc.com.np\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}