{"id":49,"date":"2022-09-07T15:26:14","date_gmt":"2022-09-07T15:26:14","guid":{"rendered":"https:\/\/www.unioviedo.es\/compnum\/?page_id=49"},"modified":"2022-09-09T10:19:30","modified_gmt":"2022-09-09T10:19:30","slug":"unit-1-finite-arithmetic-and-error-analysis","status":"publish","type":"page","link":"https:\/\/www.unioviedo.es\/compnum\/index.php\/unit-1-finite-arithmetic-and-error-analysis\/","title":{"rendered":"Unit 1. Finite arithmetic and error analysis"},"content":{"rendered":"\n<p>1.&nbsp;Binary to decimal<br>&nbsp; &nbsp;&nbsp;Decimal to binary<\/p>\n\n\n\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T1_Ex01.html\">Exercise 1.1.1:<\/a><\/strong>&nbsp;Binary to decimal and vice versa<\/p>\n\n\n\n<hr class=\"wp-block-separator alignwide has-alpha-channel-opacity\"\/>\n\n\n\n<p>2.\u00a0The IEEE 754 standard<br>\u00a0 \u00a0 Normalized format<br>\u00a0 \u00a0 Exponent representation<br>\u00a0 \u00a0 Binary32 (single precision)<br>\u00a0 \u00a0 Binary64 (double precision)<\/p>\n\n\n\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T1_Ex03.html\">Exercise 1.2.1:<\/a><\/strong>&nbsp;Binary to decimal, single-precision<br><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T1_Ex04.html\">Exercise 1.2.2:<\/a><\/strong>&nbsp;Decimal to binary, single-precision<\/p>\n\n\n\n<hr class=\"wp-block-separator alignwide has-alpha-channel-opacity\"\/>\n\n\n\n<p>3.\u00a0\u00a0Normal numbers<br>\u00a0 \u00a0 \u00a0Subnormal numbers<br>\u00a0 \u00a0 \u00a0Machine epsilon<br>\u00a0 \u00a0 \u00a0Rounding errors<br>\u00a0 \u00a0 \u00a0Maximum integer<br>\u00a0 \u00a0 \u00a0Special values<\/p>\n\n\n\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T1_Ex05.html\">Exercise 1.3.1:<\/a><\/strong>&nbsp;Examples with a toy IEEE 754 format<br><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T1_Ex07.html\">Exercise 1.3.2:<\/a><\/strong>&nbsp;Examples with a&nbsp;simple IEEE 754 format and decimal to binary and vice versa for this format<\/p>\n\n\n\n<hr class=\"wp-block-separator alignwide has-alpha-channel-opacity\"\/>\n\n\n\n<p>4.&nbsp;Absolute and relative error<\/p>\n\n\n\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T1_Ex09.html\">Exercise 1.4.1:<\/a><\/strong>&nbsp;Calculation of absolute and relative errors<\/p>\n\n\n\n<hr class=\"wp-block-separator alignwide has-alpha-channel-opacity\"\/>\n\n\n\n<p>5. IEEE 754 standard rounding<\/p>\n\n\n\n<p><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T1_Ex10.html\">Exercise 1.5.1:<\/a>&nbsp;<\/strong>Truncation and rounding to the closest even number in decimal and binary<br><strong><a href=\"https:\/\/www.unioviedo.es\/compnum\/Ejercicios_html\/T1_Ex12.html\">Exercise 1.5.2:<\/a>&nbsp;<\/strong>Conversion and rounding from decimal to single precision<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1.&nbsp;Binary to decimal&nbsp; &nbsp;&nbsp;Decimal to binary Exercise 1.1.1:&nbsp;Binary to decimal and vice versa 2.\u00a0The IEEE 754 standard\u00a0 \u00a0 Normalized format\u00a0 \u00a0 Exponent representation\u00a0 \u00a0 Binary32 (single precision)\u00a0 \u00a0 Binary64 (double precision) Exercise 1.2.1:&nbsp;Binary to decimal, single-precisionExercise 1.2.2:&nbsp;Decimal to binary, single-precision 3.\u00a0\u00a0Normal numbers\u00a0 \u00a0 \u00a0Subnormal numbers\u00a0 \u00a0 \u00a0Machine epsilon\u00a0 \u00a0 \u00a0Rounding errors\u00a0 \u00a0 \u00a0Maximum integer\u00a0 \u00a0 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-49","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/pages\/49","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/comments?post=49"}],"version-history":[{"count":10,"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/pages\/49\/revisions"}],"predecessor-version":[{"id":320,"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/pages\/49\/revisions\/320"}],"wp:attachment":[{"href":"https:\/\/www.unioviedo.es\/compnum\/index.php\/wp-json\/wp\/v2\/media?parent=49"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}