{"id":160312,"date":"2023-09-25T15:56:27","date_gmt":"2023-09-25T10:26:27","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160312"},"modified":"2023-09-25T15:56:27","modified_gmt":"2023-09-25T10:26:27","slug":"the-size-of-the-physical-address-space-of-a-processor-is-2%f0%9d%91%83-bytes","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/the-size-of-the-physical-address-space-of-a-processor-is-2%f0%9d%91%83-bytes\/","title":{"rendered":"The size of the physical address space of a processor is 2\ud835\udc43 bytes"},"content":{"rendered":"\n

Q. The size of the physical address space of a processor is 2\ud835\udc43<\/sup> bytes. The word length is 2\ud835\udc4a<\/sup> bytes. The capacity of cache memory is 2\ud835\udc41<\/sup> bytes. The size of each cache block is 2\ud835\udc40<\/sup> words. For a \ud835\udc3e-way set-associative cache memory, the length (in number of bits) of the tag field is<\/p>\n\n\n\n

(A) \ud835\udc43 \u2212 \ud835\udc41 \u2212 log2<\/sub> \ud835\udc3e                                          (B) \ud835\udc43 \u2212 \ud835\udc41 + log2<\/sub> \ud835\udc3e<\/p>\n\n\n\n

(C) \ud835\udc43 \u2212 \ud835\udc41 \u2212 \ud835\udc40 \u2212 \ud835\udc4a \u2212 log2<\/sub> \ud835\udc3e                          (D) \ud835\udc43 \u2212 \ud835\udc41 \u2212 \ud835\udc40 \u2212 \ud835\udc4a + log2<\/sub> \ud835\udc3e<\/p>\n\n\n\n

Ans: \ud835\udc43 \u2212 \ud835\udc41 + log2<\/sub> \ud835\udc3e<\/p>\n\n\n\n

Sol:<\/p>\n\n\n\n

Physical Address Space = 2P<\/sup> Bytes. Word Length is 2W<\/sup> bytes, which means each word is of size 2W<\/sup> bytes.
Cache memory size = 2N<\/sup> Bytes and Tag Size = 2X<\/sup> Bytes.
Physical address is P \u2013 W bits
Number of blocks in cache = 2(N-W-M)<\/sup><\/p>\n\n\n\n

It is a K-way set associative cache memory, each set in cache will have K-blocks.
So, Number of sets = 2(N-W-M)<\/sup>\/ K
SET bits will be N-W-M-logk
Offset bits will be M<\/p>\n\n\n\n

We know,
TAG bits = Main memory bits \u2013 SET bits \u2013 offset bits<\/strong>
So, TAG bits(x) = P \u2013 W \u2013 (N-M-W-logk)- M
\u00a0 \u00a0 \u00a0 = P \u2013 W \u2013 N + M + W + logk \u2013 M
\u00a0 \u00a0 \u00a0 x = P \u2013 N + logk<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Q. The size of the physical address space of a processor is 2\ud835\udc43 bytes. The word length is 2\ud835\udc4a bytes. The capacity of cache memory is 2\ud835\udc41 bytes. The size of each cache block is 2\ud835\udc40 words. For a \ud835\udc3e-way set-associative cache memory, the length (in number of bits) of the tag field is (A) […]<\/p>\n","protected":false},"author":419,"featured_media":160313,"comment_status":"open","ping_status":"","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-160312","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\/160312","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=160312"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160312\/revisions"}],"predecessor-version":[{"id":160314,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160312\/revisions\/160314"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160313"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160312"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160312"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160312"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}