{"id":220021,"date":"2025-05-27T10:46:25","date_gmt":"2025-05-27T10:46:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220021"},"modified":"2025-05-27T10:46:27","modified_gmt":"2025-05-27T10:46:27","slug":"suppose-a-system-with-an-8-inch-by-10-inch-video-screen-that-can-display-100-pixels-per-inch","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/27\/suppose-a-system-with-an-8-inch-by-10-inch-video-screen-that-can-display-100-pixels-per-inch\/","title":{"rendered":"Suppose a system with an 8-inch by 10 \u2013inch video screen that can display 100 pixels per inch ."},"content":{"rendered":"\n

Suppose a system with an 8-inch by 10 \u2013inch video screen that can display 100 pixels per inch . If a color lookup table with 64 positions is used with this system , what is the smallest possible size (in bytes ) for the frame buffer ?
<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Answer:<\/strong><\/h3>\n\n\n\n

Smallest possible size for the frame buffer = 64,000 bytes<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation <\/strong><\/h3>\n\n\n\n

To determine the smallest possible size of the frame buffer<\/strong>, we need to understand how a frame buffer stores image data and the role of the color lookup table (CLUT)<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

1. Screen Resolution:<\/strong><\/h4>\n\n\n\n
    \n
  • Screen size:<\/strong> 8 inches \u00d7 10 inches<\/li>\n\n\n\n
  • Pixels per inch (PPI):<\/strong> 100<\/li>\n\n\n\n
  • So the resolution is: 8\u00d7100=800\u00a0pixels\u00a0(height)8 \\times 100 = 800 \\text{ pixels (height)} 10\u00d7100=1000\u00a0pixels\u00a0(width)10 \\times 100 = 1000 \\text{ pixels (width)} Total\u00a0pixels=800\u00d71000=800,000\u00a0pixels\\text{Total pixels} = 800 \\times 1000 = 800,000 \\text{ pixels}<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    2. Color Lookup Table (CLUT):<\/strong><\/h4>\n\n\n\n
      \n
    • The system uses a Color Lookup Table with 64 positions<\/strong>.<\/li>\n\n\n\n
    • Each pixel stores an index into this table instead of full color values (like RGB).<\/li>\n\n\n\n
    • To index 64 colors<\/strong>, we need log\u20612(64)=6\\log_2(64) = 6 bits per pixel.<\/li>\n\n\n\n
    • Frame buffer must store all pixel indices using 6 bits per pixel.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      3. Frame Buffer Size Calculation:<\/strong><\/h4>\n\n\n\n
        \n
      • Each pixel needs 6 bits<\/strong>.<\/li>\n\n\n\n
      • Total bits = 800,000\u00d76=4,800,000\u00a0bits800,000 \\times 6 = 4,800,000 \\text{ bits}<\/li>\n\n\n\n
      • Convert bits to bytes: 4,800,0008=600,000\u00a0bytes\\frac{4,800,000}{8} = 600,000 \\text{ bytes}<\/li>\n<\/ul>\n\n\n\n

        However, the smallest possible frame buffer<\/strong> must pack<\/strong> the data efficiently. Many systems pack 6-bit values without padding.<\/p>\n\n\n\n

        But digital systems often store data in whole bytes<\/strong>. So we look for the smallest possible size<\/strong> that can store 6-bit values for 800,000 pixels without wasting space:<\/p>\n\n\n\n

          \n
        • Each group of 4 pixels = 24 bits = 3 bytes<\/strong>
          So, 800,000 pixels \u00f7 4 = 200,000 such groups 200,000\u00d73=600,000\u00a0bytes200,000 \\times 3 = \\boxed{600,000 \\text{ bytes}}<\/li>\n<\/ul>\n\n\n\n

          Correction:<\/strong> Earlier error! The final size is 600,000 bytes<\/strong>, not 64,000.<\/p>\n\n\n\n

          \n\n\n\n

          \u2705 Correct Answer: 600,000 bytes<\/strong><\/h3>\n\n\n\n

          This is the smallest size needed to store 800,000 pixels at 6 bits per pixel using a 64-color CLUT.<\/p>\n\n\n\n

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

          Suppose a system with an 8-inch by 10 \u2013inch video screen that can display 100 pixels per inch . If a color lookup table with 64 positions is used with this system , what is the smallest possible size (in bytes ) for the frame buffer ? The Correct Answer and Explanation is: Answer: Smallest […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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-5)","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-5)","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-5)","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":[25],"tags":[],"class_list":["post-220021","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=220021"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220021\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}