{"id":156180,"date":"2022-03-26T01:28:15","date_gmt":"2022-03-25T19:58:15","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/bases-explanation-counting-in-different-bases-and-faqs\/"},"modified":"2022-12-22T21:37:27","modified_gmt":"2022-12-22T16:07:27","slug":"bases-explanation-counting-in-different-bases-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/bases\/","title":{"rendered":"Bases &#8211; Explanation, Counting in Different Bases, and FAQs"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Number_Bases\" title=\"Number Bases\">Number Bases<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#What_is_a_Base_Number\" title=\"What is a Base Number?\">What is a Base Number?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_2_Number_System\" title=\"Base 2 Number System\">Base 2 Number System<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Counting_in_Different_Bases\" title=\"Counting in Different Bases\">Counting in Different Bases<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Let_us_Understand_How_to_do_Counting_in_Different_Base\" title=\"Let us Understand How to do Counting in Different Base\">Let us Understand How to do Counting in Different Base<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_2_Binary_Number_System_Has_Only_2_Digits_0_and_1\" title=\"(Base 2) Binary Number System Has Only 2 Digits: 0 and 1\">(Base 2) Binary Number System Has Only 2 Digits: 0 and 1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_3_Ternary_Number_System_Has_3_Digits_01_and_2\" title=\"(Base 3) Ternary Number System Has 3 Digits: 0,1, and 2\">(Base 3) Ternary Number System Has 3 Digits: 0,1, and 2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_4_Quaternary_Number_System_Has_4_Digits_0_1_2_and_3\" title=\"(Base 4) Quaternary Number System Has 4 Digits: 0, 1, 2, and 3\">(Base 4) Quaternary Number System Has 4 Digits: 0, 1, 2, and 3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_5_Quinary_Number_System_Has_5_Digits_0_1_2_3_and_4\" title=\"(Base 5) Quinary Number System Has 5 Digits: 0, 1, 2, 3, and 4\">(Base 5) Quinary Number System Has 5 Digits: 0, 1, 2, 3, and 4<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_6_Senary_Number_System_Has_6_Digits_0_1_2_3_4_and_5\" title=\"(Base 6) Senary Number System Has 6 Digits: 0, 1, 2, 3, 4, and 5\">(Base 6) Senary Number System Has 6 Digits: 0, 1, 2, 3, 4, and 5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_7_Septenary_Number_System_Has_7_Digits_0_1_2_3_4_5_and_6\" title=\"(Base 7) Septenary Number System Has 7 Digits: 0, 1, 2, 3, 4, 5, and 6\">(Base 7) Septenary Number System Has 7 Digits: 0, 1, 2, 3, 4, 5, and 6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_8_Octal_Number_System_Has_8_Digits_0_1_2_3_4_5_6_and_7\" title=\"(Base 8) Octal Number System Has 8 Digits: 0, 1, 2, 3, 4, 5, 6, and 7\">(Base 8) Octal Number System Has 8 Digits: 0, 1, 2, 3, 4, 5, 6, and 7<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Nonary_Base_9_Number_System_Has_9_Digits_0_1_2_3_4_5_6_7_and_8\" title=\"Nonary (Base 9) Number System Has 9 Digits: 0, 1, 2, 3, 4, 5, 6, 7, and 8\">Nonary (Base 9) Number System Has 9 Digits: 0, 1, 2, 3, 4, 5, 6, 7, and 8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/bases\/#Base_10_Decimal_Number_System_Has_10_Digits_0_1_2_3_4_5_6_7_9_and_10\" title=\"(Base 10) Decimal Number System Has 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 9, and 10\">(Base 10) Decimal Number System Has 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 9, and 10<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Number_Bases\"><\/span>Number Bases<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are a few number systems that are used in mathematics and computer science. The two most common are base 10 and base 2. In base 10, the number 26 is written as 2\u00d710+6. This means that 26 is two 10s added together, with 6 leftover. In base 2, the number 26 is written as 11010. This means that 26 is 11010 in binary.<\/p>\n<p>Base 10 is the number system that we use in everyday life. It uses the digits 0-9. In base 2, the number 26 is written as 11010. This means that 26 is 11010 in binary. The binary number system uses the digits 0 and 1. The number 26 is two 10s added together, with 6 leftover.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156179 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/bases-explanation-counting-in-different-bases-and-faqs.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/bases-explanation-counting-in-different-bases-and-faqs.jpg?v=1648238290 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/bases-explanation-counting-in-different-bases-and-faqs-300x212.jpg?v=1648238290 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Base_Number\"><\/span>What is a Base Number?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A base number is a number that is used as a multiplier in a particular number system. The most common number system in use today is the base 10 number system, which uses the digits 0 through 9. In the base 10 number system, the number 10 is the base number. This means that the number 10 can be multiplied by any other number to produce a result in base 10. For example, the number 12 can be expressed as 1 \u00d7 10 + 2 \u00d7 1, or 1,200 in base 10.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_2_Number_System\"><\/span>Base 2 Number System<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The base 2 number system is a numeral system that uses only the digits 0 and 1. It is a positional numeral system, meaning that the position of a digit determines its value. In the base 2 number system, the value of a digit is 1 multiplied by the power of 2 that corresponds to the position of the digit. For example, the value of the digit 1 in the number 1101 is 1 multiplied by 2 to the third power, or 8. The value of the digit 1 in the number 101 is 1 multiplied by 2 to the second power, or 4.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Counting_in_Different_Bases\"><\/span>Counting in Different Bases<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Base 10<\/p>\n<p>One, two, three, four, five, six, seven, eight, nine, ten.<\/p>\n<p>Base 2<\/p>\n<p>One, two, three, four, five, six, seven, eight, nine, ten.<\/p>\n<p>Base 16<\/p>\n<p>One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Let_us_Understand_How_to_do_Counting_in_Different_Base\"><\/span>Let us Understand How to do Counting in Different Base<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Base 10 counting:<\/p>\n<p>In base 10 counting, the number system we use everyday, the number 10 is used as a base. The number 10 can be represented by the number 1 followed by 0 zeroes. So, the number 10 can also be represented as 1,000. In this number system, every number can be represented by a combination of 1s and 0s. For example, the number 12 can be represented as 1,000 + 2,000, or 1,100 + 1,000.<\/p>\n<p>Base 2 counting:<\/p>\n<p>In base 2 counting, the number 2 is used as a base. The number 2 can be represented by the number 1 followed by 1 zero. So, the number 2 can also be represented as 10. In this number system, every number can be represented by a combination of 1s and 0s. For example, the number 11 can be represented as 1,000 + 1,000 + 1, or 1,001.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_2_Binary_Number_System_Has_Only_2_Digits_0_and_1\"><\/span>(Base 2) Binary Number System Has Only 2 Digits: 0 and 1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The binary number system has only 2 digits: 0 and 1. In the binary number system, every number is represented by a combination of 0s and 1s. For example, the number 12 can be represented by the combination of 1, 2, and 0:<\/p>\n<p>1<br \/>\n+<br \/>\n2<br \/>\n=<br \/>\n3<\/p>\n<p>In the binary number system, the number 1 is represented by the combination of 0 and 1, and the number 2 is represented by the combination of 1 and 1. The number 3 is represented by the combination of 1, 2, and 0, and the number 4 is represented by the combination of 0 and 1, and so on.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_3_Ternary_Number_System_Has_3_Digits_01_and_2\"><\/span>(Base 3) Ternary Number System Has 3 Digits: 0,1, and 2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The ternary number system (base 3) has three digits: 0, 1, and 2. The ternary number system is a positional numeral system with a base of 3. It uses three symbols: 0, 1, and 2. In the ternary number system, the number 123 represents 1\u00d7102 + 2\u00d7101 + 3\u00d7100, or 1+2+3=6.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_4_Quaternary_Number_System_Has_4_Digits_0_1_2_and_3\"><\/span>(Base 4) Quaternary Number System Has 4 Digits: 0, 1, 2, and 3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>0000<br \/>\n0001<br \/>\n0002<br \/>\n0003<\/p>\n<p>0010<br \/>\n0011<br \/>\n0100<br \/>\n0101<br \/>\n0110<br \/>\n0111<br \/>\n1000<br \/>\n1001<br \/>\n1010<br \/>\n1011<br \/>\n1100<br \/>\n1101<br \/>\n1110<br \/>\n1111<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_5_Quinary_Number_System_Has_5_Digits_0_1_2_3_and_4\"><\/span>(Base 5) Quinary Number System Has 5 Digits: 0, 1, 2, 3, and 4<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>6 (Base 10) Hexadecimal Number System Has 16 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F<\/p>\n<p>Base 16, or hexadecimal, is a number system that has 16 digits. The digits in hexadecimal are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15. Hexadecimal is used in computer programming, because it is a convenient way to represent binary numbers.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_6_Senary_Number_System_Has_6_Digits_0_1_2_3_4_and_5\"><\/span>(Base 6) Senary Number System Has 6 Digits: 0, 1, 2, 3, 4, and 5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The senary number system is a base-6 number system that uses the digits 0, 1, 2, 3, 4, and 5. It is a positional system, meaning that the value of a digit depends on its position within the number. In the senary number system, the number 12345 would be written as 54321.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_7_Septenary_Number_System_Has_7_Digits_0_1_2_3_4_5_and_6\"><\/span>(Base 7) Septenary Number System Has 7 Digits: 0, 1, 2, 3, 4, 5, and 6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Octal Number System Has 8 Digits: 0, 1, 2, 3, 4, 5, 6, and 7<\/p>\n<p>Nonary Number System Has 9 Digits: 0, 1, 2, 3, 4, 5, 6, 7, and 8<\/p>\n<p>Binary Number System Has 2 Digits: 0 and 1<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_8_Octal_Number_System_Has_8_Digits_0_1_2_3_4_5_6_and_7\"><\/span>(Base 8) Octal Number System Has 8 Digits: 0, 1, 2, 3, 4, 5, 6, and 7<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The octal number system is a base 8 number system. This means that the number system uses 8 digits: 0, 1, 2, 3, 4, 5, 6, and 7. In the octal number system, these digits represent the following powers of 8:<\/p>\n<p>0: 1<br \/>\n1: 8<br \/>\n2: 64<br \/>\n3: 512<br \/>\n4: 4096<br \/>\n5: 32768<br \/>\n6: 262144<br \/>\n7: 2097152<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Nonary_Base_9_Number_System_Has_9_Digits_0_1_2_3_4_5_6_7_and_8\"><\/span>Nonary (Base 9) Number System Has 9 Digits: 0, 1, 2, 3, 4, 5, 6, 7, and 8<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The number 9 is not used in the base 9 number system.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Base_10_Decimal_Number_System_Has_10_Digits_0_1_2_3_4_5_6_7_9_and_10\"><\/span>(Base 10) Decimal Number System Has 10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 9, and 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The number 123 can be represented in the decimal number system as 1, 2, 3, 10, 11, 12.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Number Bases There are a few number systems that are used in mathematics and computer science. The two most common [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Bases - Explanation, Counting in Different Bases, and FAQs","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about bases topic of maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","custom_permalink":"maths\/bases\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Bases - Explanation, Counting in Different Bases, and FAQs - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about bases topic of maths in details explained by subject experts on infinitylearn.com. 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