{"id":210332,"date":"2025-04-30T08:10:22","date_gmt":"2025-04-30T08:10:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=210332"},"modified":"2025-04-30T08:10:26","modified_gmt":"2025-04-30T08:10:26","slug":"what-is-the-largest-binary-number-that-can-be-expressed-with-16-bits","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/04\/30\/what-is-the-largest-binary-number-that-can-be-expressed-with-16-bits\/","title":{"rendered":"What is the largest binary number that can be expressed with 16 bits"},"content":{"rendered":"\n<p>a. What is the largest binary number that can be expressed with 16 bits? (Provide the answer in binary i.e., something like 1100111100011110)<\/p>\n\n\n\n<p>b. What is the equivalent of the number in decimal? (Provide the value in decimal i.e., something like 9276)<\/p>\n\n\n\n<p>c. What is the equivalent of the number in hexadecimal? (Provide the value in hexadecimal i.e., something like 9F2A)<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s solve the problem step by step:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>a. What is the largest binary number that can be expressed with 16 bits?<\/strong><\/h3>\n\n\n\n<p>The largest binary number with 16 bits is:<\/p>\n\n\n\n<p><strong>1111111111111111<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>b. What is the equivalent of the number in decimal?<\/strong><\/h3>\n\n\n\n<p>This binary number in decimal is:<\/p>\n\n\n\n<p><strong>65,535<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>c. What is the equivalent of the number in hexadecimal?<\/strong><\/h3>\n\n\n\n<p>This binary number in hexadecimal is:<\/p>\n\n\n\n<p><strong>FFFF<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Detailed Explanation (300+ Words)<\/strong><\/h3>\n\n\n\n<p>A <strong>bit<\/strong> is the smallest unit of data in computing and represents a binary digit: either 0 or 1. A <strong>16-bit number<\/strong> means the number is represented using 16 binary digits (bits).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>a. Largest 16-bit Binary Number:<\/strong><\/h4>\n\n\n\n<p>When all 16 bits are set to 1, we get the largest possible binary number for that bit length. That is:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">CopyEdit<code>1111111111111111\n<\/code><\/pre>\n\n\n\n<p>This is equivalent to having all the binary &#8220;places&#8221; filled with the highest possible value (1), similar to writing 9999 in decimal for a 4-digit number.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>b. Decimal Equivalent:<\/strong><\/h4>\n\n\n\n<p>To convert this binary number to decimal, we use powers of 2. Each position in a binary number represents a power of 2, starting from the rightmost bit (2\u2070) to the leftmost bit (2\u00b9\u2075 for 16 bits).<\/p>\n\n\n\n<p>Mathematically:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">CopyEdit<code>= 2\u2070 + 2\u00b9 + 2\u00b2 + ... + 2\u00b9\u2075\n= 1 + 2 + 4 + 8 + 16 + ... + 32768\n= 65,535\n<\/code><\/pre>\n\n\n\n<p>This is the maximum value you can store using <strong>unsigned 16-bit binary<\/strong>, meaning there is no sign bit (i.e., only positive values).<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>c. Hexadecimal Equivalent:<\/strong><\/h4>\n\n\n\n<p>Hexadecimal is a base-16 number system, using digits 0\u20139 and letters A\u2013F. Each group of <strong>4 binary bits<\/strong> (a nibble) converts to one hexadecimal digit.<\/p>\n\n\n\n<p>Break 16-bit binary into 4 groups:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">yamlCopyEdit<code>1111 1111 1111 1111\n<\/code><\/pre>\n\n\n\n<p>Each group of 4 bits equals:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1111 = F (15 in decimal)<\/li>\n<\/ul>\n\n\n\n<p>So, the 16-bit binary number is:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">scssCopyEdit<code>FFFF (hexadecimal)\n<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">\u2705 Summary:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Binary<\/strong>: 1111111111111111<\/li>\n\n\n\n<li><strong>Decimal<\/strong>: 65535<\/li>\n\n\n\n<li><strong>Hexadecimal<\/strong>: FFFF<\/li>\n<\/ul>\n\n\n\n<p>This concept is widely used in computing, particularly in defining memory addresses, data types, and setting register limits in microprocessors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>a. What is the largest binary number that can be expressed with 16 bits? (Provide the answer in binary i.e., something like 1100111100011110) b. What is the equivalent of the number in decimal? (Provide the value in decimal i.e., something like 9276) c. What is the equivalent of the number in hexadecimal? (Provide the value [&hellip;]<\/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-210332","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/210332","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=210332"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/210332\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=210332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=210332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=210332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}