{"id":7711,"date":"2022-04-15T17:47:45","date_gmt":"2022-04-15T12:17:45","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7711"},"modified":"2025-06-02T20:51:40","modified_gmt":"2025-06-02T15:21:40","slug":"what-is-a-number-system-in-digital-electronics","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-a-number-system-in-digital-electronics\/","title":{"rendered":"What is a number system in digital electronics?"},"content":{"rendered":"\n<ul class=\"wp-block-list\"><li>A number system is a way of writing any number.<\/li><li>It can be represented by using any symbols or digits.<\/li><li>It provides distinctive representation for each number.<\/li><li>We can calculate value of any <a href=\"https:\/\/en.wikipedia.org\/wiki\/Digit\">digit<\/a> with the help of its position and base value.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Decimal Number System<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>This is the most commonly used number system with base value of ten.<\/li><li>It uses ten digits from 0 to 9.<\/li><li>The leftmost position from decimal is units, tens, hundred and so on.<\/li><li>The number 5312 has 2 in units place, 1 in tens place, 3 in hundreds place and 5 in thousands place.<\/li><li>We can also express the number as<\/li><\/ul>\n\n\n\n<p>(5\u00d71000) + (3\u00d7100) + (1\u00d710) + (2\u00d7l)<\/p>\n\n\n\n<p>=(5\u00d710<sup>3<\/sup>) + (3\u00d710<sup>2<\/sup>) + (1\u00d710<sup>1<\/sup>) + (2\u00d7l0<sup>0<\/sup>)<\/p>\n\n\n\n<p>=5000 + 300 + 10 + 2<\/p>\n\n\n\n<p>=5312<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Binary Number System<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>This number system has only two digits 0 and 1.<\/li><li>The base of the binary number system is 2.<\/li><li>The position of each number is the power of the base.<\/li><\/ul>\n\n\n\n<p>Convert 10101<sub>2<\/sub> to decimal number?<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Step<\/strong><\/td><td><strong>Binary Number<\/strong><\/td><td><strong>Decimal Number<\/strong><\/td><\/tr><tr><td>Step 1<\/td><td>10101<sub>2<\/sub><\/td><td>((1 \u00d7 2<sup>4<\/sup>) + (0 \u00d7 2<sup>3<\/sup>) + (1 \u00d7 2<sup>2<\/sup>) + (0 \u00d7 2<sup>1<\/sup>) + (1 \u00d7 2<sup>0<\/sup>))<sub>10<\/sub><\/td><\/tr><tr><td>Step 2<\/td><td>10101<sub>2<\/sub><\/td><td>(16 + 0 + 4 + 0 + 1)<sub>10<\/sub><\/td><\/tr><tr><td>Step 3<\/td><td>10101<sub>2<\/sub><\/td><td>21<sub>10<\/sub><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Note:<\/strong> We can write 10111<sub>2<\/sub> as 10111.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Octal Number System<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>The base value of this number system is eight.<\/li><li>It has total eight digits from 0 to 7. <\/li><li>Therefore we call it the octal number systems.<\/li><li>The position of each number is the power of the base.<\/li><\/ul>\n\n\n\n<p>Convert 12569<sub>8<\/sub> to decimal number?<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Step<\/strong><\/td><td><strong>Octal Number<\/strong><\/td><td><strong>Decimal Number<\/strong><\/td><\/tr><tr><td>Step 1<\/td><td>12569<sub>8<\/sub><\/td><td>((1 \u00d7 8<sup>4<\/sup>) + (2 \u00d7 8<sup>3<\/sup>) + (5 \u00d7 8<sup>2<\/sup>) + (6 \u00d7 8<sup>1<\/sup>) + (9 \u00d7 8<sup>0<\/sup>))<sub>10<\/sub><\/td><\/tr><tr><td>Step 2<\/td><td>12569<sub>8<\/sub><\/td><td>(4096 + 1024 + 320 + 48 + 9)<sub>10<\/sub><\/td><\/tr><tr><td>Step 3<\/td><td>12569<sub>8<\/sub><\/td><td>5497<sub>10<\/sub><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Note:<\/strong> We can write 12575<sub>8<\/sub> as 12575 in octal.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Hexadecimal Number Systems<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>This number system consists of ten digits and six letters.<\/li><li>The digits are 0-9 and letters A-F.<\/li><li>The value of these letters in the form of numbers is given as A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.<\/li><li>The base value of this number system is sixteen.<\/li><li>The position of each number is equal to the power of the base.<\/li><\/ul>\n\n\n\n<p>Convert 19FBA<sub>16<\/sub> to decimal number?<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Step<\/strong><\/td><td><strong>Hexadecimal Number<\/strong><\/td><td><strong>Decimal Number<\/strong><\/td><\/tr><tr><td>Step 1<\/td><td>19FBA<sub>16<\/sub><\/td><td>((1 \u00d7 16<sup>4<\/sup>) + (9 \u00d7 16<sup>3<\/sup>) + (F \u00d7 16<sup>2<\/sup>) + (B \u00d7 16<sup>1<\/sup>) + (A \u00d7 16<sup>0<\/sup>))<sub>10<\/sub><\/td><\/tr><tr><td>Step 2<\/td><td>19FBA<sub>16<\/sub><\/td><td>((1 \u00d7 16<sup>4<\/sup>) + (9 \u00d7 16<sup>3<\/sup>) + (15 \u00d7 16<sup>2<\/sup>) + (11 \u00d7 16<sup>1<\/sup>) + (10 \u00d7 16<sup>0<\/sup>))<sub>10<\/sub><\/td><\/tr><tr><td>Step 3<\/td><td>19FBA<sub>16<\/sub><\/td><td>(65536 + 36864 + 3840 + 176 + 10)<sub>10<\/sub><\/td><\/tr><tr><td>Step 4<\/td><td>19FDA<sub>16<\/sub><\/td><td>106426<sub>10<\/sub><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Note:<\/strong> We can write 19FDA<sub>16<\/sub> as 19FDA in hexadecimal.<\/p>\n\n\n\n<p><strong>Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-the-state-transition-matrix\/\">Properties of State transition matrix?<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-are-encoders-and-decoders\/\" target=\"_blank\" rel=\"noreferrer noopener\">Encoders and Decoders<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-uart\/\" target=\"_blank\" rel=\"noreferrer noopener\">Working of UART<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-fft\/\" target=\"_blank\" rel=\"noreferrer noopener\">Classification of FFT<\/a><\/li><li><a href=\"https:\/\/www.goseeko.com\/blog\/what-is-fourier-transform\/\" target=\"_blank\" rel=\"noreferrer noopener\">Fourier Transform and its properties<\/a><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A number system is a way of writing any number. It can be represented by using any symbols or digits. It provides distinctive representation.<\/p>\n","protected":false},"author":3,"featured_media":7718,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[37],"tags":[],"class_list":["post-7711","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electronics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is a number system in digital electronics? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"A number system is a way of writing any number. It can be represented by using any symbols or digits. 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