{"id":3222,"date":"2025-06-06T08:33:07","date_gmt":"2025-06-06T08:33:07","guid":{"rendered":"https:\/\/diznr.com\/?p=3222"},"modified":"2025-06-06T08:33:07","modified_gmt":"2025-06-06T08:33:07","slug":"day-06part-10-operating-system-for-gate-examples-based-on-multiplicative-and-modulo-additive","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-06part-10-operating-system-for-gate-examples-based-on-multiplicative-and-modulo-additive\/","title":{"rendered":"Day 06Part 10 &#8211; Operating System for gate-Examples based on multiplicative and additive modulo"},"content":{"rendered":"<p>Day 06Part 10 &#8211; Operating System for gate-Examples based on multiplicative and additive modulo<\/p>\n<p>[fvplayer id=&#8221;305&#8243;]<\/p>\n<p data-start=\"0\" data-end=\"280\">It looks like you&#8217;re looking for <strong data-start=\"33\" data-end=\"96\">Operating System (OS) concepts related to modulo operations<\/strong> for <strong data-start=\"101\" data-end=\"121\">GATE preparation<\/strong>. However, <strong data-start=\"132\" data-end=\"170\">multiplicative and additive modulo<\/strong> are more commonly associated with <strong data-start=\"205\" data-end=\"247\">Discrete Mathematics and Number Theory<\/strong> rather than Operating Systems.<\/p>\n<p data-start=\"282\" data-end=\"329\">Could you clarify whether you&#8217;re looking for:<\/p>\n<ol data-start=\"330\" data-end=\"637\">\n<li data-start=\"330\" data-end=\"432\"><strong data-start=\"333\" data-end=\"378\">Modulo operations in Discrete Mathematics<\/strong> (e.g., in Cryptography, Hashing, or Number Theory).<\/li>\n<li data-start=\"433\" data-end=\"553\"><strong data-start=\"436\" data-end=\"478\">Modulo operations in Operating Systems<\/strong> (e.g., in Scheduling Algorithms, Page Replacement, or Clock Algorithms).<\/li>\n<li data-start=\"554\" data-end=\"637\"><strong data-start=\"557\" data-end=\"613\">Examples of OS problems related to modulo arithmetic<\/strong> for GATE preparation.<\/li>\n<\/ol>\n<p data-start=\"639\" data-end=\"699\" data-is-last-node=\"\" data-is-only-node=\"\">Let me know, and I&#8217;ll provide the most relevant material!<\/p>\n<p data-start=\"0\" data-end=\"112\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Modular arithmetic is a fundamental concept in computer science and plays a significant role in various areas, including operating systems, cryptography, and algorithm design.<\/span> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Understanding modular addition and multiplication is crucial for solving problems related to hashing, memory addressing, and synchronization mechanisms.<\/span><\/p>\n<hr data-start=\"114\" data-end=\"117\" \/>\n<h3 data-start=\"119\" data-end=\"142\">\ud83d\udd39 Modular Addition<\/h3>\n<p data-start=\"144\" data-end=\"236\"><strong data-start=\"144\" data-end=\"159\">Definition:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">In modular addition, the sum of two integers wraps around upon reaching a certain value, known as the modulus. The operation is defined as:<\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">GeeksforGeeks<\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"639\" data-end=\"699\" data-is-last-node=\"\" data-is-only-node=\"\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(a+b)mod\u2009\u2009n(a + b) \\mod n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"260\" data-end=\"351\"><strong data-start=\"260\" data-end=\"272\">Example:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Let&#8217;s consider modulus <span class=\"katex\"><span class=\"katex-mathml\">n=7n = 7<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><\/span><\/span><\/span>:<\/span><\/p>\n<ul data-start=\"353\" data-end=\"475\">\n<li data-start=\"353\" data-end=\"394\">\n<p data-start=\"355\" data-end=\"394\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">(3+5)mod\u2009\u20097=8mod\u2009\u20097=1(3 + 5) \\mod 7 = 8 \\mod 7 = 1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"395\" data-end=\"475\">\n<p data-start=\"397\" data-end=\"475\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">(6+4)mod\u2009\u20097=10mod\u2009\u20097=3(6 + 4) \\mod 7 = 10 \\mod 7 = 3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">6<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">Math Sites UNCG<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"477\" data-end=\"492\"><strong data-start=\"477\" data-end=\"492\">Properties:<\/strong><\/p>\n<ul data-start=\"494\" data-end=\"650\">\n<li data-start=\"494\" data-end=\"552\">\n<p data-start=\"496\" data-end=\"552\"><strong data-start=\"496\" data-end=\"512\">Commutative:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">a+bmod\u2009\u2009n=b+amod\u2009\u2009na + b \\mod n = b + a \\mod n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"553\" data-end=\"650\">\n<p data-start=\"555\" data-end=\"650\"><strong data-start=\"555\" data-end=\"571\">Associative:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">(a+b)+cmod\u2009\u2009n=a+(b+c)mod\u2009\u2009n(a + b) + c \\mod n = a + (b + c) \\mod n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">GeeksforGeeks<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"652\" data-end=\"655\" \/>\n<h3 data-start=\"657\" data-end=\"686\">\ud83d\udd38 Modular Multiplication<\/h3>\n<p data-start=\"688\" data-end=\"782\"><strong data-start=\"688\" data-end=\"703\">Definition:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Modular multiplication involves multiplying two integers and then taking the modulus:<\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">GeeksforGeeks<\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"639\" data-end=\"699\" data-is-last-node=\"\" data-is-only-node=\"\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(a\u00d7b)mod\u2009\u2009n(a \\times b) \\mod n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"811\" data-end=\"902\"><strong data-start=\"811\" data-end=\"823\">Example:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">With modulus <span class=\"katex\"><span class=\"katex-mathml\">n=7n = 7<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><\/span><\/span><\/span>:<\/span><\/p>\n<p data-start=\"811\" data-end=\"902\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">(3\u00d74)mod\u2009\u20097=12mod\u2009\u20097=5(3 \\times 4) \\mod 7 = 12 \\mod 7 = 5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">3<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">12<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"904\" data-end=\"1026\">\n<li data-start=\"946\" data-end=\"1026\">\n<p data-start=\"948\" data-end=\"1026\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">(5\u00d76)mod\u2009\u20097=30mod\u2009\u20097=2(5 \\times 6) \\mod 7 = 30 \\mod 7 = 2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">5<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">30<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">Math Sites UNCG<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<p data-start=\"1028\" data-end=\"1043\"><strong data-start=\"1028\" data-end=\"1043\">Properties:<\/strong><\/p>\n<ul data-start=\"1045\" data-end=\"1275\">\n<li data-start=\"1045\" data-end=\"1103\">\n<p data-start=\"1047\" data-end=\"1103\"><strong data-start=\"1047\" data-end=\"1063\">Commutative:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">a\u00d7bmod\u2009\u2009n=b\u00d7amod\u2009\u2009na \\times b \\mod n = b \\times a \\mod n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"1104\" data-end=\"1162\">\n<p data-start=\"1106\" data-end=\"1162\"><strong data-start=\"1106\" data-end=\"1122\">Associative:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">(a\u00d7b)\u00d7cmod\u2009\u2009n=a\u00d7(b\u00d7c)mod\u2009\u2009n(a \\times b) \\times c \\mod n = a \\times (b \\times c) \\mod n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li data-start=\"1163\" data-end=\"1275\">\n<p data-start=\"1165\" data-end=\"1275\"><strong data-start=\"1165\" data-end=\"1196\">Distributive over addition:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">a\u00d7(b+c)mod\u2009\u2009n=(a\u00d7b+a\u00d7c)mod\u2009\u2009na \\times (b + c) \\mod n = (a \\times b + a \\times c) \\mod n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1277\" data-end=\"1280\" \/>\n<h3 data-start=\"1282\" data-end=\"1322\">\ud83d\udd39 Applications in Operating Systems<\/h3>\n<p data-start=\"1324\" data-end=\"1402\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Modular arithmetic is utilized in various aspects of operating systems:<\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">Mathematics LibreTexts<\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1404\" data-end=\"1695\">\n<li data-start=\"1404\" data-end=\"1465\">\n<p data-start=\"1406\" data-end=\"1465\"><strong data-start=\"1406\" data-end=\"1425\">Hash Functions:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Used in hash tables for indexing and quick data retrieval.<\/span><\/p>\n<\/li>\n<li data-start=\"1466\" data-end=\"1530\">\n<p data-start=\"1468\" data-end=\"1530\"><strong data-start=\"1468\" data-end=\"1490\">Memory Management:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Calculating addresses in circular buffers or ring buffers.<\/span><\/p>\n<\/li>\n<li data-start=\"1531\" data-end=\"1596\">\n<p data-start=\"1533\" data-end=\"1596\"><strong data-start=\"1533\" data-end=\"1556\">Process Scheduling:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Determining time slices and managing cyclic queues.<\/span><\/p>\n<\/li>\n<li data-start=\"1597\" data-end=\"1695\">\n<p data-start=\"1599\" data-end=\"1695\"><strong data-start=\"1599\" data-end=\"1616\">Cryptography:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Implementing encryption algorithms that rely on modular operations.<\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1697\" data-end=\"1700\" \/>\n<h3 data-start=\"1702\" data-end=\"1726\">\ud83d\udd38 Practice Problems<\/h3>\n<ol data-start=\"1728\" data-end=\"2036\">\n<li data-start=\"1728\" data-end=\"1881\">\n<p data-start=\"1731\" data-end=\"1783\"><strong data-start=\"1731\" data-end=\"1743\">Problem:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Compute <span class=\"katex\"><span class=\"katex-mathml\">(9+8)mod\u2009\u20097(9 + 8) \\mod 7<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">9<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1787\" data-end=\"1881\">\n<li data-start=\"1787\" data-end=\"1881\">\n<p data-start=\"1789\" data-end=\"1881\"><strong data-start=\"1789\" data-end=\"1802\">Solution:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">17mod\u2009\u20097=317 \\mod 7 = 3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">17<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">Math Sites UNCG<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"1883\" data-end=\"2036\">\n<p data-start=\"1886\" data-end=\"1938\"><strong data-start=\"1886\" data-end=\"1898\">Problem:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Compute <span class=\"katex\"><span class=\"katex-mathml\">(4\u00d75)mod\u2009\u20097(4 \\times 5) \\mod 7<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">4<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mclose\">)<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1942\" data-end=\"2036\">\n<li data-start=\"1942\" data-end=\"2036\">\n<p data-start=\"1944\" data-end=\"2036\"><strong data-start=\"1944\" data-end=\"1957\">Solution:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><span class=\"katex\"><span class=\"katex-mathml\">20mod\u2009\u20097=620 \\mod 7 = 6<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">20<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathrm\">mod<\/span><\/span><span class=\"mord\">7<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">6<\/span><\/span><\/span><\/span><\/span><span class=\"ms-1 inline-flex max-w-full items-center relative top-[-0.094rem] animate-[show_150ms_ease-in]\"><span class=\"relative start-0 bottom-0 flex h-full w-full items-center\"><span class=\"flex h-4 w-full items-center justify-between overflow-hidden\"><span class=\"max-w-full grow truncate overflow-hidden text-center\">Math Sites UNCG<\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<hr data-start=\"2038\" data-end=\"2041\" \/>\n<h3 data-start=\"2043\" data-end=\"2065\">\ud83d\udcda Further Reading<\/h3>\n<ul data-start=\"2067\" data-end=\"2391\">\n<li data-start=\"2067\" data-end=\"2156\">\n<p data-start=\"2069\" data-end=\"2156\"><a class=\"cursor-pointer\" target=\"_new\" rel=\"noopener\" data-start=\"2069\" data-end=\"2156\">Modular Arithmetic &#8211; GeeksforGeeks<\/a><\/p>\n<\/li>\n<li data-start=\"2157\" data-end=\"2241\">\n<p data-start=\"2159\" data-end=\"2241\">Modular Arithmetic &#8211; Wikipedia<\/p>\n<\/li>\n<li data-start=\"2242\" data-end=\"2391\">\n<p data-start=\"2244\" data-end=\"2391\">Modular Arithmetic &#8211; Khan Academy<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"2393\" data-end=\"2396\" \/>\n<p data-start=\"2398\" data-end=\"2516\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Understanding modular arithmetic is essential for tackling various problems in computer science and operating systems.<\/span> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">It provides a foundation for designing efficient algorithms and managing system resources effectively.<\/span><\/p>\n<p data-start=\"2518\" data-end=\"2589\">If you need more examples or have specific questions, feel free to ask!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Day 06Part 10 &#8211; Operating System for gate-Examples based on multiplicative and additive modulo [fvplayer id=&#8221;305&#8243;] It looks like you&#8217;re looking for Operating System (OS) concepts related to modulo operations for GATE preparation. However, multiplicative and additive modulo are more commonly associated with Discrete Mathematics and Number Theory rather than Operating Systems. Could you clarify [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[78],"tags":[],"class_list":["post-3222","post","type-post","status-publish","format-standard","hentry","category-operating-system"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3222","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=3222"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3222\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}