{"id":4149,"date":"2026-10-21T10:08:37","date_gmt":"2026-10-21T09:08:37","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matematik\/buyuk-sayi-hesaplayici\/"},"modified":"2026-10-21T10:08:37","modified_gmt":"2026-10-21T09:08:37","slug":"buyuk-sayi-hesaplayici","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/buyuk-sayi-hesaplayici\/","title":{"rendered":"B\u00fcy\u00fck say\u0131 hesaplay\u0131c\u0131"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">\u00c7ok b\u00fcy\u00fck say\u0131larla kesin aritmetik<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"4149\" data-favorite-title=\"B\u00fcy\u00fck say\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/buyuk-sayi-hesaplayici\/\" data-favorite-excerpt=\"Dev say\u0131larla tam aritmetik sunar: toplama, \u00e7\u0131karma, \u00e7arpma, b\u00f6lme, kuvvet, fakt\u00f6riyel, karek\u00f6k, EBOB ve EKOK \u2014 say\u0131 ba\u015f\u0131na 1.000 basama\u011fa kadar, kayan nokta yuvarlamas\u0131 olmadan. Bir i\u015flem se\u00e7in, iki say\u0131 girin ve sonucun t\u00fcm basamaklar\u0131n\u0131 g\u00f6r\u00fcn.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-arithmetic\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/matematik\/buyuk-sayi-hesaplayici\/\" method=\"POST\" class=\"calculator\" id=\"calculator-4149\" data-post=\"4149\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">\u0130\u015flem<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"lem\"><option value=\"add\">a + b (toplama)<\/option><option value=\"sub\">a \u2212 b (\u00e7\u0131karma)<\/option><option value=\"mul\" selected>a \u00d7 b (\u00e7arpma)<\/option><option value=\"div\">a \u00f7 b (b\u00f6lme)<\/option><option value=\"mod\">a mod b (kalan)<\/option><option value=\"pow\">x ^ y (kuvvet)<\/option><option value=\"sqrt\">\u221ax (karek\u00f6k)<\/option><option value=\"fact\">n! (fakt\u00f6riyel)<\/option><option value=\"gcd\">EBOB(a, b)<\/option><option value=\"lcm\">EKOK(a, b)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Birinci say\u0131 (a)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"birinci_say_a\" id=\"field-2\" aria-describedby=\"calc-info-2\" placeholder=\"\u00f6rn. 2, 2.5, 1e100 veya -3.2e50\" step=\"any\" value=\"123456789012345678901234567890\"\/><small id=\"calc-info-2\">Tam say\u0131, ondal\u0131k say\u0131 (nokta veya virg\u00fcl) ya da 3.2e50 veya \u22121.7E\u221230 gibi bilimsel g\u00f6sterim. \u00dcs i\u015faretinden \u00f6nce en fazla 1.000 basamak; \u00fcs en fazla \u00b110.000 olabilir.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">\u0130kinci say\u0131 (b)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"kinci_say_b\" id=\"field-3\" aria-describedby=\"calc-info-3\" placeholder=\"e.g. 7, 0.125, 4.5e-30\" step=\"any\" value=\"987654321098765432109876543210\"\/><small id=\"calc-info-3\">\u0130kinci i\u015flenen, ayn\u0131 bi\u00e7imde. x ^ y i\u00e7in 0 ile 10.000 aras\u0131nda bir tam say\u0131 girin; \u221ax ve n! i\u00e7in bu alan kullan\u0131lmaz.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Ondal\u0131k basamak (\u00f7 ve \u221a)<\/label><div class=\"term\">P<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"ondalk_basamak_ve_\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" max=\"10000\" value=\"25\"\/><small id=\"calc-info-4\">a \u00f7 b i\u00e7in kullan\u0131l\u0131r: b\u00f6l\u00fcm\u00fcn ondal\u0131k basamak say\u0131s\u0131, 5 ve \u00fczeri yukar\u0131 yuvarlan\u0131r \u2014 hesap makinesi, b\u00f6lmenin tam olarak \u00e7\u0131k\u0131p \u00e7\u0131kmad\u0131\u011f\u0131n\u0131 da belirtir. \u221ax i\u00e7in kullan\u0131l\u0131r: k\u00f6k\u00fcn ondal\u0131k basamak say\u0131s\u0131.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"4149\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Sonu\u00e7<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Sonu\u00e7taki anlaml\u0131 basamak say\u0131s\u0131<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Bilimsel g\u00f6sterim<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Kesin mi, yuvarlanm\u0131\u015f m\u0131?<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-5\"><span class=\"field-title\"><span>Sonu\u00e7 nas\u0131l hesapland\u0131<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"4149\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>B\u00fcy\u00fck say\u0131 form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ x = \\frac{V}{10^{S}}, \\qquad a \\times b = \\frac{V_a \\cdot V_b}{10^{S_a + S_b}}, \\qquad a \\pm b = \\frac{V_a \\cdot 10^{\\,s - S_a} \\pm V_b \\cdot 10^{\\,s - S_b}}{10^{s}}, \\quad s = \\max(S_a, S_b) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(V\\) \u2014 say\u0131n\u0131n t\u00fcm basamaklar\u0131n\u0131n tek bir kesin BigInt tamsay\u0131s\u0131 olarak yaz\u0131lm\u0131\u015f h\u00e2li (1.000 basama\u011fa kadar)<\/li>\n<li>\\(S\\) \u2014 ondal\u0131k \u00f6l\u00e7ek: \\(x = V\/10^S\\); \u00f6rne\u011fin 2,5 say\u0131s\u0131 25\/10, 0,125 say\u0131s\u0131 ise 125\/1000 olarak saklan\u0131r<\/li>\n<li>\\(s\\) \u2014 toplama, \u00e7\u0131karma, kalan, EBOB ve EKOK i\u015flemleri i\u00e7in iki i\u015fleneni hizalayan ortak \u00f6l\u00e7ek<\/li>\n<\/ul>\n<p>Her giri\u015f \u00f6l\u00e7ekli bir tamsay\u0131 olarak yeniden yaz\u0131ld\u0131\u011f\u0131 i\u00e7in on i\u015flemin t\u00fcm\u00fc tamamen kesin tamsay\u0131 aritmeti\u011fiyle y\u00fcr\u00fct\u00fcl\u00fcr; ondal\u0131k ayra\u00e7 yaln\u0131zca sonucu g\u00f6sterirken geri eklenir. \u00c7arpma, toplama, kuvvet, fakt\u00f6riyel, EBOB ve EKOK her zaman tamd\u0131r; b\u00f6lme ve karek\u00f6k ise istenen ondal\u0131k basamakta yar\u0131m ve \u00fczeri yukar\u0131 yuvarlan\u0131r ve sonu\u00e7 kutusu bunu belirtir.<\/p>\n<p>\r\n<\/section>\n<p>\ufffd<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>B\u00fcy\u00fck say\u0131 \u2013 hesaplama \u00f6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \u0130\u015flem <em>a \u00d7 b (\u00e7arpma)<\/em> olarak se\u00e7ilmi\u015f, varsay\u0131lan giri\u015fler: a = 123456789012345678901234567890 ve b = 987654321098765432109876543210.<\/p>\n<p>\\[ 123456789012345678901234567890 \\times 987654321098765432109876543210 = 121\\,932\\,631\\,137\\,021\\,795\\,226\\,185\\,032\\,733\\,622\\,923\\,332\\,237\\,463\\,801\\,111\\,263\\,526\\,900 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> 121932631137021795226185032733622923332237463801111263526900 \u2014 kesin 60 basamakl\u0131 bir \u00e7arp\u0131m; 60 anlaml\u0131 basamak olarak raporlan\u0131r ve bilimsel g\u00f6sterimde 1,2193263114 \u00d7 10<sup>59<\/sup> de\u011ferine e\u015fittir. Bir kayan nokta hesaplay\u0131c\u0131s\u0131 bu basamaklar\u0131n yaln\u0131zca ilk 15\u201317'sini koruyabilirdi.<\/p>\n<p>\n\r\n<\/section><\/p>\n<h2>B\u00fcy\u00fck say\u0131 hesaplay\u0131c\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li><strong>\u0130\u015flem<\/strong> \u2014 a\u00e7\u0131l\u0131r listeden on i\u015flemden birini se\u00e7in: toplama, \u00e7\u0131karma, \u00e7arpma, b\u00f6lme, kalan (mod), kuvvet, karek\u00f6k, fakt\u00f6riyel, EBOB veya EKOK.<\/li>\n<li><strong>Birinci say\u0131 (a)<\/strong> \u2014 en fazla 1.000 basamak girin: bir tamsay\u0131, nokta ya da virg\u00fcll\u00fc bir ondal\u0131k say\u0131 veya <code>3.2e50<\/code>, <code>-1.7E-30<\/code> gibi bilimsel g\u00f6sterimde bir say\u0131. \u221ax i\u00e7in bu say\u0131 x'i, n! i\u00e7in n'yi g\u00f6sterir.<\/li>\n<li><strong>\u0130kinci say\u0131 (b)<\/strong> \u2014 ayn\u0131 bi\u00e7imde ikinci i\u015flenen. <em>x ^ y<\/em> i\u015fleminde 0 ile 10.000 aras\u0131nda bir tam say\u0131 olmal\u0131d\u0131r; \u221ax ve n! i\u015flemlerinde kullan\u0131lmad\u0131\u011f\u0131 i\u00e7in bu alan gizlenir.<\/li>\n<li><strong>Ondal\u0131k basamak (\u00f7 ve \u221a)<\/strong> \u2014 b\u00f6l\u00fcm\u00fcn ya da karek\u00f6k\u00fcn ka\u00e7 ondal\u0131k basamak g\u00f6stermesini istedi\u011finizi ayarlay\u0131n (0 ile 10.000 aras\u0131). Bu alan yaln\u0131zca bu iki i\u015flemde g\u00f6r\u00fcn\u00fcr.<\/li>\n<li>Sonu\u00e7lar\u0131 okuyun: kopyalama d\u00fc\u011fmesiyle birlikte tam <strong>Sonu\u00e7<\/strong>, <strong>Sonu\u00e7taki anlaml\u0131 basamak say\u0131s\u0131<\/strong>, 11 anlaml\u0131 basamakl\u0131 <strong>Bilimsel g\u00f6sterim<\/strong>, <strong>Tam m\u0131, yuvarlanm\u0131\u015f m\u0131?<\/strong> karar\u0131 ve <strong>Sonucun nas\u0131l hesapland\u0131\u011f\u0131na<\/strong> ili\u015fkin a\u00e7\u0131klama notu.<\/li>\n<\/ol>\n<h2>\u0130\u015flemler bir bak\u0131\u015fta<\/h2>\n<table>\n<thead>\n<tr>\n<th>\u0130\u015flem<\/th>\n<th>\u0130kinci say\u0131 (b)<\/th>\n<th>Ondal\u0131k basamak<\/th>\n<th>Sonu\u00e7<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>a + b, a \u2212 b, a \u00d7 b<\/td>\n<td>kullan\u0131l\u0131r<\/td>\n<td>kullan\u0131lmaz<\/td>\n<td>her zaman tamd\u0131r<\/td>\n<\/tr>\n<tr>\n<td>a \u00f7 b (b\u00f6lme)<\/td>\n<td>kullan\u0131l\u0131r, 0 olamaz<\/td>\n<td>0\u201310.000<\/td>\n<td>m\u00fcmk\u00fcnse tamd\u0131r; aksi h\u00e2lde yar\u0131m ve \u00fczeri yukar\u0131 yuvarlan\u0131r ve yuvarland\u0131\u011f\u0131 belirtilir<\/td>\n<\/tr>\n<tr>\n<td>a mod b (kalan)<\/td>\n<td>kullan\u0131l\u0131r, 0 olamaz<\/td>\n<td>kullan\u0131lmaz<\/td>\n<td>tamd\u0131r; i\u015faret birinci say\u0131y\u0131 izler<\/td>\n<\/tr>\n<tr>\n<td>x ^ y (kuvvet)<\/td>\n<td>0\u201310.000 aras\u0131 tam say\u0131<\/td>\n<td>kullan\u0131lmaz<\/td>\n<td>tamd\u0131r (x<sup>0<\/sup> = 1, kural gere\u011fi 0<sup>0<\/sup> = 1)<\/td>\n<\/tr>\n<tr>\n<td>\u221ax (karek\u00f6k)<\/td>\n<td>gizli<\/td>\n<td>0\u201310.000<\/td>\n<td>tam karelerde tamd\u0131r, aksi h\u00e2lde yar\u0131m ve \u00fczeri yukar\u0131 yuvarlan\u0131r<\/td>\n<\/tr>\n<tr>\n<td>n! (fakt\u00f6riyel)<\/td>\n<td>gizli<\/td>\n<td>kullan\u0131lmaz<\/td>\n<td>tamd\u0131r, n = 0\u20135.000 i\u00e7in<\/td>\n<\/tr>\n<tr>\n<td>EBOB(a, b), EKOK(a, b)<\/td>\n<td>kullan\u0131l\u0131r<\/td>\n<td>kullan\u0131lmaz<\/td>\n<td>tamd\u0131r; ondal\u0131kl\u0131 say\u0131lara izin verilir<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Tam b\u00fcy\u00fck say\u0131 aritmeti\u011fi neden \u00f6nemlidir?<\/h2>\n<p>S\u0131radan hesap makineleri ve elektronik tablolar say\u0131lar\u0131 64 bit IEEE 754 kayan nokta de\u011ferleri olarak saklar; bu de\u011ferler yaln\u0131zca yakla\u015f\u0131k 15\u201317 anlaml\u0131 ondal\u0131k basamak tutabilir. Bundan sonras\u0131 sessizce yuvarlan\u0131r: \u00e7o\u011fu sistemde <code>1e20 + 1<\/code> i\u015fleminin sonucu tam olarak <code>1e20<\/code> \u00e7\u0131kar ve 60 basamakl\u0131 bir \u00e7arp\u0131m en fazla 17 do\u011fru basamak korur. Bu yuvarlama ekranda g\u00f6r\u00fcnmez ama ger\u00e7ektir ve sonraki her hesapta birikerek b\u00fcy\u00fcr \u2014 b\u00fcy\u00fck bir \u00e7arp\u0131m\u0131 denetlemeniz, kombinasyonlar\u0131 sayman\u0131z ya da bir algoritmay\u0131 basamak basamak kontrol etmeniz gerekti\u011finde ciddi bir sorun olur.<\/p>\n<p>Bu hesaplay\u0131c\u0131 kayan noktay\u0131 tamamen atlar. Her giri\u015f, bir BigInt tamsay\u0131s\u0131 \\(V\\) ve bir ondal\u0131k \u00f6l\u00e7ek \\(S\\) olarak yeniden yaz\u0131l\u0131r; toplama, \u00e7arpma, karelerle \u00fcs alma, Newton iterasyonuyla karek\u00f6k, EBOB i\u00e7in \u00d6klid algoritmas\u0131 ve terim terim \u00e7arp\u0131lan fakt\u00f6riyel dahil her i\u015flem bu tamsay\u0131lar \u00fczerinde, 15\u201317 basamak s\u0131n\u0131r\u0131 olmadan y\u00fcr\u00fct\u00fcl\u00fcr. Yuvarlaman\u0131n olabilece\u011fi tek yer, istenen ondal\u0131k basamaktaki b\u00f6lme ve karek\u00f6kt\u00fcr; <strong>Tam m\u0131, yuvarlanm\u0131\u015f m\u0131?<\/strong> kutusu hangi durumda oldu\u011funuzu a\u00e7\u0131k\u00e7a belirtir; \u00f6yleyse \u201cTam\u201d karar\u0131 ekranda g\u00f6rd\u00fc\u011f\u00fcn\u00fcz her tek basama\u011f\u0131n do\u011fru oldu\u011fu anlam\u0131na gelir.<\/p>\n<p>Kalan \u00e7\u0131kt\u0131 kutular\u0131 uzun sonu\u00e7lar\u0131 y\u00f6netmenize yard\u0131mc\u0131 olur: <strong>Sonu\u00e7taki anlaml\u0131 basamak say\u0131s\u0131<\/strong> uzunlu\u011fu tam olarak verir; <strong>Bilimsel g\u00f6sterim<\/strong> b\u00fcy\u00fckl\u00fc\u011f\u00fc 11 anlaml\u0131 basama\u011fa g\u00f6re g\u00f6sterir \u2014 boyutlar\u0131 kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in kullan\u0131\u015fl\u0131d\u0131r ve <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/bilimsel-gosterim-hesaplayici\/\">bilimsel g\u00f6sterim d\u00f6n\u00fc\u015ft\u00fcr\u00fcc\u00fc<\/a> ile kolayca d\u00f6n\u00fc\u015ft\u00fcr\u00fclebilir. Tipik kullan\u0131mlar aras\u0131nda b\u00fcy\u00fck \u00e7arp\u0131mlar\u0131n elle denetlenmesi, kombinatorik hesaplar, dev say\u0131larla ev \u00f6devlerinin do\u011frulanmas\u0131 ve \u00e7ift duyarl\u0131kl\u0131 bir arac\u0131n yan\u0131t\u0131n\u0131z\u0131 sessizce yuvarlayaca\u011f\u0131 her t\u00fcrl\u00fc g\u00f6rev say\u0131labilir.<\/p>\n<h2>S\u0131n\u0131rlar, kurallar ve pratik ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Girdi boyutu:<\/strong> her say\u0131 \u00fcsten \u00f6nce en fazla 1.000 basamak i\u00e7erebilir; \u00fcs en fazla \u00b110.000 olabilir. 1.000.000 basamaktan uzun sonu\u00e7lar, sayfay\u0131 dondurmak yerine bir uyar\u0131yla reddedilir.<\/li>\n<li><strong>Kuvvet ve fakt\u00f6riyel:<\/strong> x ^ y i\u015fleminde \u00fcs 0 ile 10.000 aras\u0131nda bir tam say\u0131 olmal\u0131d\u0131r (negatif kuvvetler sonlu olmayan kesirler verir ve kabul edilmez); n!, 0 ile 5.000 aras\u0131ndaki tam say\u0131lar\u0131 kabul eder. Daha k\u00fc\u00e7\u00fck n de\u011ferleri i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/faktoriyel-hesaplama\/\">fakt\u00f6riyel hesaplay\u0131c\u0131<\/a> ad\u0131m ad\u0131m \u00e7arp\u0131m\u0131 g\u00f6sterir.<\/li>\n<li><strong>B\u00f6lme ve k\u00f6kler:<\/strong> a \u00f7 b, istenen ondal\u0131k basamaklara g\u00f6re yar\u0131m ve \u00fczeri yukar\u0131 yuvarlan\u0131r; hesaplay\u0131c\u0131 b\u00f6lmenin tam \u00e7\u0131k\u0131p \u00e7\u0131kmad\u0131\u011f\u0131n\u0131 bildirir. \u221ax \u00f6nce x'in sonlu bir ondal\u0131k say\u0131n\u0131n karesi olup olmad\u0131\u011f\u0131n\u0131 denetler; de\u011filse k\u00f6k yar\u0131m ve \u00fczeri yukar\u0131 yuvarlan\u0131r ve i\u015faretlenir.<\/li>\n<li><strong>Kalan\u0131n i\u015fareti:<\/strong> a mod b, JavaScript ve C'deki % i\u015fleci gibi birinci say\u0131n\u0131n i\u015faretini al\u0131r. Her zaman negatif olmayan (\u00d6klid) kalana ihtiyac\u0131n\u0131z varsa, sonu\u00e7 negatif \u00e7\u0131kt\u0131\u011f\u0131nda |b| ekleyerek d\u00fczeltin.<\/li>\n<li><strong>Ondal\u0131kl\u0131 say\u0131larda EBOB ve EKOK:<\/strong> iki i\u015flenen de \u00f6nce ortak bir on kuvvetine \u00f6l\u00e7eklenir; bu y\u00fczden EBOB(2,5; 1,5) = 0,5 do\u011fal bi\u00e7imde \u00e7al\u0131\u015f\u0131r. G\u00fcnl\u00fck tamsay\u0131lar i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/ebob-hesaplama\/\">EBOB hesaplay\u0131c\u0131y\u0131<\/a> da kullanabilirsiniz.<\/li>\n<li><strong>Mod\u00fcler aritmetik:<\/strong> yaln\u0131zca x ^ y mod m de\u011ferine ihtiyac\u0131n\u0131z varsa, <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/moduler-us-alma-hesaplama\/\">mod\u00fcler \u00fcs alma hesaplay\u0131c\u0131s\u0131<\/a> devasa kuvveti ba\u015ftan olu\u015fturma gereksinimini ortadan kald\u0131r\u0131r.<\/li>\n<li><strong>Bi\u00e7imlendirme:<\/strong> ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta da virg\u00fcl de kullanabilirsiniz, ancak ikisini asla ayn\u0131 say\u0131da bir arada kullanmay\u0131n; eksi i\u015faretleri ve bo\u015fluklar otomatik olarak temizlenir. Sonu\u00e7larda ASCII eksi i\u015fareti kullan\u0131l\u0131r; b\u00f6ylece ba\u015fka ara\u00e7lara sorunsuz yap\u0131\u015ft\u0131r\u0131l\u0131rlar ve her sonucun yan\u0131nda bir <em>Sonucu kopyala<\/em> d\u00fc\u011fmesi bulunur.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Dev say\u0131larla tam aritmetik sunar: toplama, \u00e7\u0131karma, \u00e7arpma, b\u00f6lme, kuvvet, fakt\u00f6riyel, karek\u00f6k, EBOB ve EKOK \u2014 say\u0131 ba\u015f\u0131na 1.000 basama\u011fa kadar, kayan nokta yuvarlamas\u0131 olmadan. Bir i\u015flem se\u00e7in, iki say\u0131 girin ve sonucun t\u00fcm basamaklar\u0131n\u0131 g\u00f6r\u00fcn.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[18],"class_list":["post-4149","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-aritmetik-hesap-makineleri"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4149","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=4149"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/4149\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=4149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=4149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=4149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}