{"id":65823,"date":"2026-10-14T11:50:53","date_gmt":"2026-10-14T06:20:53","guid":{"rendered":"https:\/\/www.quickonlinetips.com\/archives\/?page_id=65823"},"modified":"2026-10-15T10:49:04","modified_gmt":"2026-10-15T05:19:04","slug":"number-base-converter","status":"publish","type":"page","link":"https:\/\/www.quickonlinetips.com\/archives\/tools\/number-base-converter\/","title":{"rendered":"Number Base Converter: Binary, Decimal, Hex and Octal"},"content":{"rendered":"<p>Convert <strong>binary to decimal<\/strong>, decimal to binary, hexadecimal and octal in one place. Type a number in any box and the others update instantly. 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.qt-lb{display:inline-flex;width:44px;height:44px;border-radius:50%;align-items:center;justify-content:center;font-weight:700;font-size:17px;background:#fff;color:#1A202C;border:2px solid var(--qt-accent);margin:3px} .qt-tool .qt-lb.qt-bonus{background:#E53E3E;color:#fff;border-color:#E53E3E} .qt-tool .qt-8{width:230px;height:230px;border-radius:50%;margin:16px auto;background:radial-gradient(circle at 35% 30%,#666,#000 62%);display:flex;align-items:center;justify-content:center;cursor:pointer;box-shadow:0 10px 24px rgba(0,0,0,.35)} .qt-tool .qt-8 span{width:116px;height:116px;border-radius:50%;background:radial-gradient(circle,#2747a8,#0b1a4a);color:#fff;display:flex;align-items:center;justify-content:center;text-align:center;font-size:13px;font-weight:700;padding:16px;box-sizing:border-box;line-height:1.25;transition:opacity .3s} .qt-tool .qt-shake{animation:qt-shake .7s} @keyframes qt-shake{0%,100%{transform:translate(0)}20%{transform:translate(-12px,4px) rotate(-6deg)}40%{transform:translate(10px,-6px) rotate(5deg)}60%{transform:translate(-8px,6px) rotate(-4deg)}80%{transform:translate(6px,-3px) rotate(3deg)}} .qt-tool .qt-grid>.qt-field{display:flex;flex-direction:column;justify-content:flex-end} .qt-tool .qt-field input[type=range]{height:46px;padding:0 10px} .qt-tool .qt-field input[type=color]{height:46px} .qt-tool .qt-drop .qt-sub{font-weight:400;font-size:14px;margin:4px 0 0} .qt-tool .qt-board{display:grid;gap:5px;margin:14px auto 0;max-width:100%;user-select:none;-webkit-user-select:none;touch-action:manipulation} .qt-tool .qt-cell{display:flex;align-items:center;justify-content:center;background:#fff;border:1px solid #AEC3DB;border-radius:6px;font-weight:700;cursor:pointer;aspect-ratio:1;font-size:clamp(14px,4vw,26px);color:#1A202C;padding:0;min-width:0;font-family:inherit;line-height:1} .qt-tool .qt-cell:disabled{cursor:default} .qt-tool .qt-win{background:#C6F6D5;border-color:#38A169} .qt-tool .qt-sel{background:#BEE3F8;border-color:#3182CE} .qt-tool .qt-bad{background:#FED7D7;border-color:#E53E3E} .qt-tool select{-webkit-appearance:none;-moz-appearance:none;appearance:none;padding-right:40px;cursor:pointer;border:2px solid #90B4DA;font-weight:600;background-color:#fff;background-image:url(\"data:image\/svg+xml,%3Csvg xmlns='http:\/\/www.w3.org\/2000\/svg' viewBox='0 0 14 9'%3E%3Cpath d='M1.5 1.5l5.5 5.5 5.5-5.5' fill='none' stroke='%232B6CB0' stroke-width='2.4' stroke-linecap='round' stroke-linejoin='round'\/%3E%3C\/svg%3E\");background-repeat:no-repeat;background-position:right 14px center;background-size:14px 9px} .qt-tool select:hover{border-color:var(--qt-accent);background-color:#F4F8FD} .qt-tool select::-ms-expand{display:none} .qt-next{margin:0 0 1.75em} .qt-next .qt-next-h{font-size:14px;font-weight:700;letter-spacing:.05em;text-transform:uppercase;color:#4A5568;margin:0 0 8px} .qt-next-g{display:grid;grid-template-columns:repeat(3,1fr);gap:8px} .qt-next-g a{display:flex;align-items:center;min-height:46px;padding:9px 12px;border:1px solid #AEC3DB;border-radius:8px;background:#F4F8FD;color:#215387;font-weight:600;font-size:15px;line-height:1.3;text-decoration:none} .qt-next-g a:hover,.qt-next-g a:focus{background:#E3EEFF;border-color:#2B6CB0;text-decoration:none} @media (max-width:600px){.qt-next-g{grid-template-columns:repeat(2,1fr)}}<\/style>\n<div class=\"qt-tool\" id=\"qt-nb\">\n<div class=\"qt-grid\">\n<div class=\"qt-field\"><label for=\"qt-nb-10\">Decimal (base 10)<\/label><input type=\"text\" id=\"qt-nb-10\" value=\"2026\" spellcheck=\"false\"><\/div>\n<div class=\"qt-field\"><label for=\"qt-nb-2\">Binary (base 2)<\/label><input type=\"text\" id=\"qt-nb-2\" spellcheck=\"false\"><\/div>\n<div class=\"qt-field\"><label for=\"qt-nb-16\">Hexadecimal (base 16)<\/label><input type=\"text\" id=\"qt-nb-16\" spellcheck=\"false\"><\/div>\n<div class=\"qt-field\"><label for=\"qt-nb-8\">Octal (base 8)<\/label><input type=\"text\" id=\"qt-nb-8\" spellcheck=\"false\"><\/div>\n<div class=\"qt-field\"><label for=\"qt-nb-cb\">Other base<\/label><select id=\"qt-nb-cb\"><\/select><\/div>\n<div class=\"qt-field\"><label for=\"qt-nb-c\">Value in that base<\/label><input type=\"text\" id=\"qt-nb-c\" spellcheck=\"false\"><\/div>\n<\/div>\n<div class=\"qt-explain\" id=\"qt-nb-steps\" style=\"text-align:left\"><\/div>\n<div class=\"qt-status\" id=\"qt-nb-status\" aria-live=\"polite\"><\/div>\n<p class=\"qt-note\">Everything runs in your browser. Nothing you enter is sent to or stored on our server.<\/p>\n<\/div>\n<p><script>(function () { function qtReady(fn) { if (document.readyState === 'loading') { document.addEventListener('DOMContentLoaded', fn); } else { fn(); } } function qtCopy(text, statusEl, okMsg) { function done(ok) { if (statusEl) { statusEl.textContent = ok ? (okMsg || 'Copied to clipboard.') : 'Press Ctrl+C (or Cmd+C) to copy.'; } } function fallback() { var ta = document.createElement('textarea'); ta.value = text; ta.setAttribute('readonly', ''); ta.style.position = 'fixed'; ta.style.top = '-1000px'; document.body.appendChild(ta); ta.select(); var ok = false; try { ok = document.execCommand('copy'); } catch (e) { ok = false; } document.body.removeChild(ta); done(ok); } if (navigator.clipboard) { if (window.isSecureContext) { navigator.clipboard.writeText(text).then(function () { done(true); }, fallback); return; } } fallback(); } function qtRand32() { var c = window.crypto || window.msCrypto; if (c) { if (c.getRandomValues) { var a = new Uint32Array(1); c.getRandomValues(a); return a[0]; } } return Math.floor(Math.random() * 4294967296); } function qtRandInt(range) { if (range === 4294967296) { return qtRand32(); } var limit = Math.floor(4294967296 \/ range) * range; var x = qtRand32(); while (x >= limit) { x = qtRand32(); } return x % range; } qtReady(function () { var d = document.getElementById('qt-nb-10'); if (!d) { return; } function $(id) { return document.getElementById(id); } var DIG = '0123456789abcdefghijklmnopqrstuvwxyz', cb = $('qt-nb-cb'); for (var b = 2; 36 >= b; b++) { var o = document.createElement('option'); o.value = b; o.textContent = 'Base ' + b; if (b === 3) { o.selected = true; } cb.appendChild(o); } function parse(s, base) { s = s.trim().toLowerCase().replace(\/[\\s_,]\/g, ''); var neg = s[0] === '-'; if (neg) { s = s.slice(1); } if (base === 16) { s = s.replace(\/^0x\/, ''); } if (base === 2) { s = s.replace(\/^0b\/, ''); } if (base === 8) { s = s.replace(\/^0o\/, ''); } if (!s) { return null; } var B = BigInt(base), n = 0n; for (var i = 0; s.length > i; i++) { var v = DIG.indexOf(s[i]); if (v === -1 || v >= base) { return undefined; } n = n * B + BigInt(v); } return neg ? -n : n; } function fmt(n, base) { var s = (0n > n ? -n : n).toString(base); return (0n > n ? '-' : '') + (base === 16 ? s.toUpperCase() : s); } function show(n, src) { var st = $('qt-nb-status'); st.textContent = ''; st.classList.remove('qt-error'); if (n === undefined) { st.textContent = 'That box contains a digit that is not allowed in its base.'; st.classList.add('qt-error'); return; } if (n === null) { ['10', '2', '16', '8', 'c'].forEach(function (k) { if (k !== src) { $('qt-nb-' + k).value = ''; } }); $('qt-nb-steps').textContent = ''; return; } if (src !== '10') { d.value = fmt(n, 10); } if (src !== '2') { $('qt-nb-2').value = fmt(n, 2); } if (src !== '16') { $('qt-nb-16').value = fmt(n, 16); } if (src !== '8') { $('qt-nb-8').value = fmt(n, 8); } if (src !== 'c') { $('qt-nb-c').value = fmt(n, +cb.value); } var bin = fmt(n, 2); if (bin.length > 0) { if (17 > bin.length) { if (n >= 0n) { $('qt-nb-steps').textContent = 'Binary ' + bin + ' = ' + bin.split('').map(function (c, i) { return c + '\u00d72^' + (bin.length - 1 - i); }).join(' + ') + ' = ' + fmt(n, 10); return; } } } $('qt-nb-steps').textContent = 'Bits needed: ' + bin.replace('-', '').length + '.'; } [['10', 10], ['2', 2], ['16', 16], ['8', 8]].forEach(function (p) { $('qt-nb-' + p[0]).addEventListener('input', function () { show(parse(this.value, p[1]), p[0]); }); }); $('qt-nb-c').addEventListener('input', function () { show(parse(this.value, +cb.value), 'c'); }); cb.addEventListener('change', function () { show(parse(d.value, 10), '10'); }); show(parse(d.value, 10), '10'); }); })();<\/script><\/p>\n<div class=\"qt-next\">\n<p class=\"qt-next-h\">Try another free tool<\/p>\n<div class=\"qt-next-g\"><a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/binary-translator\/\">Binary Translator<\/a><a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/morse-code-translator\/\">Morse Code Translator<\/a><a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/roman-numeral-converter\/\">Roman Numeral Converter<\/a><a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/temperature-converter\/\">Temperature Converter<\/a><a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/length-converter\/\">Length Converter<\/a><a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/weight-converter\/\">Weight Converter<\/a><\/div>\n<\/div>\n<p><strong>Quick answer:<\/strong> To convert binary to decimal, multiply each digit by its power of 2 and add them up. 1011 = 1\u00d78 + 0\u00d74 + 1\u00d72 + 1\u00d71 = 11. To convert decimal to binary, keep dividing by 2 and read the remainders from bottom to top.<\/p>\n<h2>How to use the number base converter<\/h2>\n<p>Type in any box: decimal, binary, hexadecimal or octal. The others update immediately. Prefixes such as 0x for hex and 0b for binary are accepted, spaces and underscores are ignored, and negative numbers work. Choose <strong>Other base<\/strong> for any base from 2 to 36. Large numbers are handled exactly with no rounding.<\/p>\n<h2>Binary to decimal, step by step<\/h2>\n<ol>\n<li>Write the powers of 2 under each digit from right to left: 1, 2, 4, 8, 16, 32 and so on.<\/li>\n<li>Add the powers where the digit is 1. For 110010: 32 + 16 + 2 = 50.<\/li>\n<\/ol>\n<h2>Decimal to binary, step by step<\/h2>\n<p>Divide by 2 and note the remainder until you reach 0. For 13: 13 \u00f7 2 = 6 r1, 6 \u00f7 2 = 3 r0, 3 \u00f7 2 = 1 r1, 1 \u00f7 2 = 0 r1. Read the remainders upwards: 1101.<\/p>\n<h2>Quick reference<\/h2>\n<table class=\"qt-ref\">\n<thead>\n<tr>\n<th>Decimal<\/th>\n<th>Binary<\/th>\n<th>Hex<\/th>\n<th>Octal<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>101<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>1010<\/td>\n<td>A<\/td>\n<td>12<\/td>\n<\/tr>\n<tr>\n<td>15<\/td>\n<td>1111<\/td>\n<td>F<\/td>\n<td>17<\/td>\n<\/tr>\n<tr>\n<td>16<\/td>\n<td>10000<\/td>\n<td>10<\/td>\n<td>20<\/td>\n<\/tr>\n<tr>\n<td>255<\/td>\n<td>11111111<\/td>\n<td>FF<\/td>\n<td>377<\/td>\n<\/tr>\n<tr>\n<td>1024<\/td>\n<td>10000000000<\/td>\n<td>400<\/td>\n<td>2000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Where each base is used<\/h2>\n<ul>\n<li><strong>Binary (base 2):<\/strong> how computers store everything, as bits that are on or off.<\/li>\n<li><strong>Hexadecimal (base 16):<\/strong> a compact way to write bytes; one hex digit is 4 bits. Used for colors (#FF8800), memory addresses and MAC addresses.<\/li>\n<li><strong>Octal (base 8):<\/strong> Unix file permissions such as chmod 755.<\/li>\n<\/ul>\n<p>To turn text into binary, use the <a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/binary-translator\/\">binary translator<\/a>. For colors, try <a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/hex-to-rgb\/\">hex to RGB<\/a>.<\/p>\n<h2>FAQ<\/h2>\n<h3>What is 255 in binary?<\/h3>\n<p>11111111, the largest value in one byte.<\/p>\n<h3>Why does hex use letters?<\/h3>\n<p>Base 16 needs 16 digits, so A to F stand for 10 to 15.<\/p>\n<h2>More free tools<\/h2>\n<div class=\"qt-cards\"><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/binary-translator\/\"><strong>Binary Translator<\/strong><span>Convert text to binary code and binary back to text.<\/span><\/a><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/morse-code-translator\/\"><strong>Morse Code Translator<\/strong><span>Turn text into Morse code and back, with sound.<\/span><\/a><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/roman-numeral-converter\/\"><strong>Roman Numeral Converter<\/strong><span>Turn numbers, years and dates into Roman numerals.<\/span><\/a><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/temperature-converter\/\"><strong>Temperature Converter<\/strong><span>Celsius, Fahrenheit and Kelvin, both ways.<\/span><\/a><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/length-converter\/\"><strong>Length Converter<\/strong><span>cm, inches, feet, metres, miles and more.<\/span><\/a><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/weight-converter\/\"><strong>Weight Converter<\/strong><span>kg to lbs, grams, ounces and stones.<\/span><\/a><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/number-to-words\/\"><strong>Number to Words<\/strong><span>Write numbers in words for cheques, US or Indian style.<\/span><\/a><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/days-between-dates\/\"><strong>Days Between Dates<\/strong><span>Count days, weeks and business days between two dates.<\/span><\/a><a class=\"qt-card\" href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/age-calculator\/\"><strong>Age Calculator<\/strong><span>Your exact age in years, months and days, plus next birthday.<\/span><\/a><\/div>\n<p>See all of them on the <a href=\"https:\/\/www.quickonlinetips.com\/archives\/tools\/\">QuickOnlineTips free online tools<\/a> page and play our <a href=\"https:\/\/www.quickonlinetips.com\/archives\/games\/\">free online games<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert binary to decimal, decimal to binary, hexadecimal and octal in one place. Type a number in any box and the others update instantly. It handles very large numbers exactly and also converts to any base from 2 to 36. Decimal (base 10) Binary (base 2) Hexadecimal (base 16) Octal (base 8) Other base Value&#8230;<\/p>\n","protected":false},"author":4,"featured_media":66609,"parent":65595,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"class_list":["post-65823","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/pages\/65823","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/comments?post=65823"}],"version-history":[{"count":3,"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/pages\/65823\/revisions"}],"predecessor-version":[{"id":66457,"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/pages\/65823\/revisions\/66457"}],"up":[{"embeddable":true,"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/pages\/65595"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/media\/66609"}],"wp:attachment":[{"href":"https:\/\/www.quickonlinetips.com\/archives\/wp-json\/wp\/v2\/media?parent=65823"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}