{"id":34419,"date":"2023-09-27T14:54:00","date_gmt":"2023-09-27T14:54:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=34419"},"modified":"2023-10-03T03:12:44","modified_gmt":"2023-10-03T03:12:44","slug":"convert-hexadecimal-to-binary-definition-table-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/hexadecimal-to-binary","title":{"rendered":"Convert Hexadecimal To Binary &#8211; Definition, Table, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-2a3c70d3-3e69-41c1-84cf-ba42363572a3\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hexadecimal-to-binary#0-what-is-the-hexadecimal-to-binary-conversion>What Is the Hexadecimal to Binary Conversion?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hexadecimal-to-binary#1-hexadecimal-to-binary-conversion-table>Hexadecimal to Binary Conversion Table<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hexadecimal-to-binary#2-how-to-convert-from-hexadecimal-to-binary>How to Convert from Hexadecimal to Binary<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hexadecimal-to-binary#8-solved-examples-on-hexadecimal-to-binary-conversion>Solved Examples on Hexadecimal to Binary Conversion<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hexadecimal-to-binary#9-practice-problems-on-hexadecimal-to-binary-conversion>Practice Problems on Hexadecimal to Binary Conversion<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/hexadecimal-to-binary#10-frequently-asked-questions-about-hexadecimal-to-binary-conversion>Frequently Asked Questions about Hexadecimal to Binary Conversion<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-hexadecimal-to-binary-conversion\">What Is the Hexadecimal to Binary Conversion?<\/h2>\n\n\n\n<p><strong>Hexadecimal to binary conversion refers to finding the binary equivalent of a hexadecimal number.<\/strong> It is a conversion from base-16 number system to base-2 number system.<\/p>\n\n\n\n<p>We know that the decimal number system with base = 10 is the most commonly used number system. Let\u2019s get to know about the hexadecimal and binary <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-system\">number systems<\/a>.<\/p>\n\n\n\n<p><strong>What is a Hexadecimal Number System?<\/strong><\/p>\n\n\n\n<p>The base of a hexadecimal system is 16. It used 16 symbols given by 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F to represent all the numbers. To represent the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number\">numbers<\/a> 0-9, we simply use the same <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/digit\">digits<\/a>. To represent 10-15, we use the letters A-F.<\/p>\n\n\n\n<p>The place values in the hexadecimal number system are expressed in terms of powers of 16.<\/p>\n\n\n\n<p><strong>What is a binary decimal system?<\/strong><\/p>\n\n\n\n<p>The base of a binary system is 2. The binary numbering system uses two digits, 0 and 1, to represent all the numbers. Binary digits 0 and 1 are also called bits.&nbsp;<\/p>\n\n\n\n<p>The place values in the binary number system are expressed in terms of powers of 2.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-hexadecimal-to-binary-conversion-table\">Hexadecimal to Binary Conversion Table<\/h2>\n\n\n\n<p>Here\u2019s the hexadecimal to binary chart for quick conversions.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Decimal<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Hexadecimal<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Binary<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">00000000<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">00000001<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">00000010<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><td class=\"has-text-align-center\" data-align=\"center\">3<\/td><td class=\"has-text-align-center\" data-align=\"center\">00000011<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><td class=\"has-text-align-center\" data-align=\"center\">00000100<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><td class=\"has-text-align-center\" data-align=\"center\">00000101<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><td class=\"has-text-align-center\" data-align=\"center\">6<\/td><td class=\"has-text-align-center\" data-align=\"center\">00000110<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">7<\/td><td class=\"has-text-align-center\" data-align=\"center\">7<\/td><td class=\"has-text-align-center\" data-align=\"center\">00000111<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><td class=\"has-text-align-center\" data-align=\"center\">8<\/td><td class=\"has-text-align-center\" data-align=\"center\">00001000<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">9<\/td><td class=\"has-text-align-center\" data-align=\"center\">9<\/td><td class=\"has-text-align-center\" data-align=\"center\">00001001<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><td class=\"has-text-align-center\" data-align=\"center\">A<\/td><td class=\"has-text-align-center\" data-align=\"center\">00001010<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">11<\/td><td class=\"has-text-align-center\" data-align=\"center\">B<\/td><td class=\"has-text-align-center\" data-align=\"center\">00001011<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">12<\/td><td class=\"has-text-align-center\" data-align=\"center\">C<\/td><td class=\"has-text-align-center\" data-align=\"center\">00001100<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">13<\/td><td class=\"has-text-align-center\" data-align=\"center\">D<\/td><td class=\"has-text-align-center\" data-align=\"center\">00001101<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">14<\/td><td class=\"has-text-align-center\" data-align=\"center\">E<\/td><td class=\"has-text-align-center\" data-align=\"center\">00001110<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">15<\/td><td class=\"has-text-align-center\" data-align=\"center\">F<\/td><td class=\"has-text-align-center\" data-align=\"center\">00001111<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-how-to-convert-from-hexadecimal-to-binary\">How to Convert from Hexadecimal to Binary<\/h2>\n\n\n\n<p>There are different ways to convert a binary number into a hexadecimal number. Either we can convert using direct methods or indirect methods.&nbsp;<\/p>\n\n\n\n<p>Method 1: Hexadecimal to decimal followed by decimal to binary<\/p>\n\n\n\n<p>Method 2: Hexadecimal to binary direct conversion<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-method-1-indirect-method\">Method 1: Indirect Method<\/h2>\n\n\n\n<p>First, we convert a binary into the decimal system, and then we convert it to a hexadecimal number.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Hexadecimal to Decimal<\/strong>: To convert from hexadecimal to decimal, multiply each digit by its respective place value, and finally add the products.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Decimal to Binary<\/strong>: To convert from decimal to binary, divide the decimal number by 2 repeatedly, until the quotient is 0.<\/li>\n<\/ul>\n\n\n\n<p><strong>Example 1: <\/strong>(A2F7)<sub>16<\/sub><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"359\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/hexadecimal-to-decimal-conversion-example.png\" alt=\"Hexadecimal to decimal conversion example\" class=\"wp-image-34423\" title=\"Hexadecimal to decimal conversion example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/hexadecimal-to-decimal-conversion-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/hexadecimal-to-decimal-conversion-example-300x174.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Example 2:<\/strong> Convert from hexadecimal to Binary: (6A)<sub>16<\/sub>\u00a0<\/p>\n\n\n\n<p>Hex to decimal: Here, A = 10<\/p>\n\n\n\n<p>$(6A)_{16} = 6 \\times 16^{1} + 10 \\times 16^{0}$<\/p>\n\n\n\n<p>$(6A)_{16} = 96 + 10$<\/p>\n\n\n\n<p>$(6A)_{16} = 106_{10}$<\/p>\n\n\n\n<p><strong>Decimal to binary:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"400\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-binary-conversion-of-the-decimal-number-106.png\" alt=\"Decimal to binary conversion of the decimal number 106\" class=\"wp-image-34425\" title=\"Decimal to binary conversion of the decimal number 106\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-binary-conversion-of-the-decimal-number-106.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-to-binary-conversion-of-the-decimal-number-106-300x194.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Thus, (6A)<sub>16<\/sub> = 106<sub>10 <\/sub>= (1101010)<sub>2<\/sub><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-method-2-direct-method-hexadecimal-to-binary-using-grouping-and-conversion-table\">Method 2: Direct Method: Hexadecimal to Binary Using Grouping and Conversion Table<\/h2>\n\n\n\n<p>There are only 16 digits from 0 to 7 and A to F in the hexadecimal number system, so we can represent any digit of the hexadecimal number system using only 4 bits as follows below.<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Divide the given hexadecimal number into individual digits.<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Assign binary equivalents to each hexadecimal digit. It&#8217;s important to keep track of leading zeros when converting hexadecimal to binary to maintain the correct number of digits.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>Hexa<\/td><td>0<\/td><td>1<\/td><td>2<\/td><td>3<\/td><td>4<\/td><td>5<\/td><td>6<\/td><td>7<\/td><\/tr><tr><td>Binary<\/td><td>0000<\/td><td>0001<\/td><td>0010<\/td><td>0011<\/td><td>0100<\/td><td>0101<\/td><td>0110<\/td><td>0111<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><tbody><tr><td>Hexa<\/td><td>8<\/td><td>9<\/td><td>A<\/td><td>B<\/td><td>C<\/td><td>D<\/td><td>E<\/td><td>F<\/td><\/tr><tr><td>Binary<\/td><td>1000<\/td><td>1001<\/td><td>1010<\/td><td>1011<\/td><td>1100<\/td><td>1101<\/td><td>1110<\/td><td>1111<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Step 3: <\/strong>Replace each hexadecimal digit with its binary equivalent using the conversion table.<\/p>\n\n\n\n<p><strong>Example:<\/strong> Let&#8217;s convert the hexadecimal number &#8220;2A&#8221; to binary:<\/p>\n\n\n\n<p>&#8220;2&#8221; in hexadecimal is equivalent to &#8220;0010&#8221; in binary.<\/p>\n\n\n\n<p>&#8220;A&#8221; in hexadecimal is equivalent to &#8220;1010&#8221; in binary.<\/p>\n\n\n\n<p>Therefore, &#8220;2A&#8221; in hexadecimal is equivalent to &#8220;00101010&#8221; in binary.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"545\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/hexadecimal-to-binary-direct-conversion.png\" alt=\"Hexadecimal to binary - direct conversion\" class=\"wp-image-34426\" title=\"Hexadecimal to binary - direct conversion\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/hexadecimal-to-binary-direct-conversion.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/hexadecimal-to-binary-direct-conversion-300x264.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-hexadecimal-to-binary-conversion-involving-hexadecimal-point\">Hexadecimal to Binary Conversion Involving Hexadecimal Point<\/h2>\n\n\n\n<p>We can convert a hexadecimal number with a hexadecimal point to the binary system using the conversion table.<\/p>\n\n\n\n<p><strong>Example:<\/strong> Convert (0.A35)<sub>16<\/sub> to binary.<\/p>\n\n\n\n<p>Find the binary equivalent of each digit using the conversion table.<\/p>\n\n\n\n<p>A<sub>16<\/sub> = 1010<sub>2<\/sub><\/p>\n\n\n\n<p>3<sub>16<\/sub> = 0011<sub>2<\/sub><\/p>\n\n\n\n<p>5<sub>16<\/sub> = 0101<sub>2<\/sub><\/p>\n\n\n\n<p>(0.A35)<sub>16<\/sub><sup> <\/sup>= (0.101000110101)<sub>2<\/sub><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-hexadecimal-to-binary-conversion\">Facts about Hexadecimal to Binary Conversion<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>Each hexadecimal digit represents a group of 4 binary bits, making it a more compact representation of binary numbers.<\/li>\n\n\n\n<li>Hexadecimal to binary conversion involves converting each hexadecimal digit into its corresponding 4-bit binary representation.<\/li>\n\n\n\n<li>Hexadecimal system is particularly useful in computer systems, as it allows for easier readability and more concise representation of large binary numbers.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the hexadecimal to binary conversion and two methods to convert a hexadecimal number into binary. Let\u2019s solve a few examples and practice problems to check your understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-hexadecimal-to-binary-conversion\">Solved Examples on Hexadecimal to Binary Conversion<\/h2>\n\n\n\n<p><strong>1. Convert <\/strong>(0B)<sub>16<\/sub> <strong>into a hexadecimal number system by direct method.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>&#8220;0&#8221; in hexadecimal is equivalent to &#8220;0000&#8221; in binary.<\/p>\n\n\n\n<p>&#8220;A&#8221; in hexadecimal is equivalent to &#8220;1010&#8221; in binary.<\/p>\n\n\n\n<p>So, (0B)<sub>16<\/sub> = (00001011)<sub>2<\/sub><\/p>\n\n\n\n<p><strong>2. What is the value of <\/strong>(F2)<sub>16<\/sub> <strong>into a hexadecimal number system using the indirect method?<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>Hexadecimal to binary:<\/strong><\/p>\n\n\n\n<p>Here, F = 15<\/p>\n\n\n\n<p>$(F2)_{16} = (15 \\times 16^{1}) + (2 \\times 16^{0})$<\/p>\n\n\n\n<p>$(F2)^{16} = (15 \\times 16) + (2 \\times 1)$<\/p>\n\n\n\n<p>$(F2)_{16} = 240 + 2$<\/p>\n\n\n\n<p>$(F2)_{16} = 242_{10}$<\/p>\n\n\n\n<p><strong>Decimal to binary:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"208\" height=\"333\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-242-to-binary.png\" alt=\"Decimal 242 to binary\" class=\"wp-image-34427\" title=\"Decimal 242 to binary\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-242-to-binary.png 208w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/10\/decimal-242-to-binary-187x300.png 187w\" sizes=\"auto, (max-width: 208px) 100vw, 208px\" \/><\/figure>\n\n\n\n<p>Thus, (F2)<sub>16<\/sub> = 242<sub>10<\/sub> = (11110010)<sub>2<\/sub><\/p>\n\n\n\n<p><strong>3. Convert <\/strong>(DE)<sub>16<\/sub><strong> into the binary number system.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>D<sub>16<\/sub> = 1101<sub>2<\/sub><\/p>\n\n\n\n<p>E<sub>16<\/sub> = 1110<sub>2<\/sub>&nbsp;<\/p>\n\n\n\n<p>So, (11011110)<sub>2<\/sub> = (DE)<sub>16<\/sub><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-hexadecimal-to-binary-conversion\">Practice Problems on Hexadecimal to Binary Conversion<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Convert Hexadecimal To Binary \u2013 Definition, Table, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Convert $(F5)_{16}$ from the hexadecimal number system to the binary system.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(10010101)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(10110101)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(11110101)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(11110111)_{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $(11110101)_{2}$<br\/>$F_{16} = 1111_{2}$  and $5_{16} = 0101_{2}$<br>\r\n$(F5)_{16} = (11110101)_{2}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the value of $(7B)_{16}$ in the number system?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(01111010)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(01110011)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(11111011)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(01111011)_{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $(01111011)_{2}$<br\/>$7_{16} = 0111_{2}$ and $B_{16} = 1011_{2}$<br>\r\n$(7B)_{16} = (01111011)_{2}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Convert $(A9)_{16}$ into the binary number system.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(10101011)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(10111001)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(10101001)_{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(11101001)_{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $(10101001)_{2}$<br\/>$1010_{2} = A_{16}$  and $100_{12} =  9_{16}$<br>\r\nSo, $(10101001)_{2} = (A9)_{16}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Convert Hexadecimal To Binary \u2013 Definition, Table, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Convert Hexadecimal To Binary\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Convert $$(F5)_{16}$$ from the hexadecimal number system to the binary system.\",\n                    \"text\": \"Convert $$(F5)_{16}$$ from the hexadecimal number system to the binary system.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$F_{16} = 1111_{2}$$  and $$5_{16} = 0101_{2}$$<br>\r\n$$(F5)_{16} = (11110101)_{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(10010101)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$F_{16} = 1111_{2}$$  and $$5_{16} = 0101_{2}$$<br>\r\n$$(F5)_{16} = (11110101)_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(10110101)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$F_{16} = 1111_{2}$$  and $$5_{16} = 0101_{2}$$<br>\r\n$$(F5)_{16} = (11110101)_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(11110111)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$F_{16} = 1111_{2}$$  and $$5_{16} = 0101_{2}$$<br>\r\n$$(F5)_{16} = (11110101)_{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(11110101)_{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$F_{16} = 1111_{2}$$  and $$5_{16} = 0101_{2}$$<br>\r\n$$(F5)_{16} = (11110101)_{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$F_{16} = 1111_{2}$$  and $$5_{16} = 0101_{2}$$<br>\r\n$$(F5)_{16} = (11110101)_{2}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the value of $$(7B)_{16}$$ in the number system?\",\n                    \"text\": \"What is the value of $$(7B)_{16}$$ in the number system?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$7_{16} = 0111_{2}$$ and $$B_{16} = 1011_{2}$$<br>\r\n$$(7B)_{16} = (01111011)_{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(01111010)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$7_{16} = 0111_{2}$$ and $$B_{16} = 1011_{2}$$<br>\r\n$$(7B)_{16} = (01111011)_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(01110011)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$7_{16} = 0111_{2}$$ and $$B_{16} = 1011_{2}$$<br>\r\n$$(7B)_{16} = (01111011)_{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(11111011)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$7_{16} = 0111_{2}$$ and $$B_{16} = 1011_{2}$$<br>\r\n$$(7B)_{16} = (01111011)_{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(01111011)_{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$7_{16} = 0111_{2}$$ and $$B_{16} = 1011_{2}$$<br>\r\n$$(7B)_{16} = (01111011)_{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$7_{16} = 0111_{2}$$ and $$B_{16} = 1011_{2}$$<br>\r\n$$(7B)_{16} = (01111011)_{2}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Convert $$(A9)_{16}$$ into the binary number system.\",\n                    \"text\": \"Convert $$(A9)_{16}$$ into the binary number system.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$1010_{2} = A_{16}$$  and $$100_{12} =  9_{16}$$<br>\r\nSo, $$(10101001)_{2} = (A9)_{16}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(10101011)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$1010_{2} = A_{16}$$  and $$100_{12} =  9_{16}$$<br>\r\nSo, $$(10101001)_{2} = (A9)_{16}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(10111001)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$1010_{2} = A_{16}$$  and $$100_{12} =  9_{16}$$<br>\r\nSo, $$(10101001)_{2} = (A9)_{16}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(11101001)_{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$1010_{2} = A_{16}$$  and $$100_{12} =  9_{16}$$<br>\r\nSo, $$(10101001)_{2} = (A9)_{16}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(10101001)_{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$1010_{2} = A_{16}$$  and $$100_{12} =  9_{16}$$<br>\r\nSo, $$(10101001)_{2} = (A9)_{16}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$1010_{2} = A_{16}$$  and $$100_{12} =  9_{16}$$<br>\r\nSo, $$(10101001)_{2} = (A9)_{16}$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-about-hexadecimal-to-binary-conversion\">Frequently Asked Questions about Hexadecimal to Binary Conversion<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\"><strong>Can I convert a hexadecimal number to binary manually?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\">\n\n<p>Yes, you can manually convert a hexadecimal number to binary by substituting each hexadecimal digit with its corresponding 4-bit binary representation. However, for larger numbers, this process can become cumbersome. It is often more convenient to use online converters, calculators, or programming tools that automate the conversion process.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\"><strong>How do you convert decimal to hexadecimal?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\">\n\n<p>Divide the decimal number by 16 repeatedly, till you get the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/quotient\">quotient<\/a> value equal to zero. Write the values of the remainder\u2019s left in the reverse order to get the hexadecimal numbers.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\"><strong>How do you convert binary to hexadecimal?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-b7a2fada-3a13-4f19-9d2a-1fa97d63c9b3\">\n\n<p>The process of converting binary to hexadecimal is the reverse of converting hexadecimal to binary. Binary digits are grouped into sets of four, and each group is converted to its corresponding hexadecimal digit. This process allows for easier representation and manipulation of binary numbers in a hexadecimal format.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Hexadecimal to Binary Conversion? Hexadecimal to binary conversion refers to finding the binary equivalent of a hexadecimal number. It is a conversion from base-16 number system to base-2 number system. We know that the decimal number system with base = 10 is the most commonly used number system. Let\u2019s get to know &#8230; <a title=\"Convert Hexadecimal To Binary &#8211; Definition, Table, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/hexadecimal-to-binary\" aria-label=\"More on Convert Hexadecimal To Binary &#8211; Definition, Table, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-34419","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34419","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=34419"}],"version-history":[{"count":6,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34419\/revisions"}],"predecessor-version":[{"id":34431,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/34419\/revisions\/34431"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=34419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=34419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=34419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}