{"id":160366,"date":"2023-09-26T14:11:04","date_gmt":"2023-09-26T08:41:04","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160366"},"modified":"2023-09-26T14:11:05","modified_gmt":"2023-09-26T08:41:05","slug":"a-processor-has-16-integer-registers-r0-r1-r15-and-64-floating-point-registers-f0-f1-f63","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-processor-has-16-integer-registers-r0-r1-r15-and-64-floating-point-registers-f0-f1-f63\/","title":{"rendered":"A processor has 16 integer registers (R0, R1, .. , R15) and 64 floating point registers (F0, F1,\u2026 , F63)"},"content":{"rendered":"\n<p>Q. A processor has 16 integer registers (R0, R1, .. , R15) and 64 floating point registers (F0, F1,\u2026 , F63). It uses a 2-byte instruction format. There are four categories of instructions: Type-1, Type-2, Type-3, and Type-4. Type-1 category consists of four instructions, each with 3 integer register operands (3Rs). Type-2 category consists of eight instructions, each with 2 floating point register operands (2Fs). Type-3 category consists of fourteen instructions, each with one integer register operand and one floating point register operand (1R+1F). Type-4 category consists of N instructions, each with a floating point register operand (1F).<\/p>\n\n\n\n<p>The maximum value of N is\u00a0________<\/p>\n\n\n\n<p><strong>(A)<\/strong>\u00a032<br><strong>(B)<\/strong>\u00a064<br><strong>(C)<\/strong>\u00a0256<br><strong>(D)<\/strong>\u00a0512<\/p>\n\n\n\n<p>Ans: 32<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Given, size of instruction format is 2 byte (= 16 bits), therefore number of instruction encoding = 2<sup>16<\/sup><br>Also, total number of bits in integer operand = log<sub>2<\/sub>(16 integer registers) = 4<br>Total number of bits in floating point operand = log<sub>2<\/sub>(64 floating point registers) = 6<\/p>\n\n\n\n<p>So, number of encoding consumed:<\/p>\n\n\n\n<p>By type 1 instructions = 4\u00d72<sup>3\u00d74<\/sup>&nbsp;= 2<sup>14<\/sup><br>By type 2 instructions = 8\u00d72<sup>2\u00d76<\/sup>&nbsp;= 2<sup>15<\/sup><br>By type 3 instructions = 14\u00d72<sup>(4+6)<\/sup>&nbsp;= 14336<\/p>\n\n\n\n<p>Now, number of encoding left for type 4 instructions = 2<sup>16<\/sup>&nbsp;\u2212 (2<sup>14<\/sup>&nbsp;+ 2<sup>15<\/sup>&nbsp;+ 14336) = 2048<br>Therefore, total number of different instructions of type 4 instructions = 2048 \/64 = 32<\/p>\n\n\n\n<p>Please note that there is difference between number of different instructions and number of different encoding, a single instruction can have different encodings when the address part differs.<\/p>\n\n\n\n<p>So, answer is 32.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A processor has 16 integer registers (R0, R1, .. , R15) and 64 floating point registers (F0, F1,\u2026 , F63). It uses a 2-byte instruction format. There are four categories of instructions: Type-1, Type-2, Type-3, and Type-4. Type-1 category consists of four instructions, each with 3 integer register operands (3Rs). Type-2 category consists of [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":160367,"comment_status":"open","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-4)","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-4)","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-4)","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":[5141],"tags":[5140],"class_list":["post-160366","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160366","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=160366"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160366\/revisions"}],"predecessor-version":[{"id":160368,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160366\/revisions\/160368"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160367"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160366"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160366"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160366"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}