{"id":1061,"date":"2017-07-10T22:55:01","date_gmt":"2017-07-10T22:55:01","guid":{"rendered":"http:\/\/bryceautomation.com\/?p=1061"},"modified":"2022-11-02T17:36:01","modified_gmt":"2022-11-02T17:36:01","slug":"binary-numbering-system","status":"publish","type":"post","link":"https:\/\/bryceautomation.com\/index.php\/2017\/07\/10\/binary-numbering-system\/","title":{"rendered":"Binary Numbering System"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Introduction to the Binary Numbering System<\/h2>\n\n\n\n<p>Simply put, the Binary Numbering System is a base 2 numbering system. &nbsp; &nbsp;The only numbers available for use to count in binary are 1, and 0. &nbsp; You can think of this in many ways: &nbsp;True\/False, Yes\/No, or High\/Low. &nbsp; &nbsp;Computers work by using the Binary numbering system, because computers only consist of billions of on\/off switches.<\/p><div id=\"bryce-1974708220\" class=\"bryce-afterfirst bryce-entity-placement\"><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-8316758073402323\" crossorigin=\"anonymous\"><\/script><ins class=\"adsbygoogle\" style=\"display:block;\" data-ad-client=\"ca-pub-8316758073402323\" \ndata-ad-slot=\"7728240895\" \ndata-ad-format=\"auto\"><\/ins>\n<script> \n(adsbygoogle = window.adsbygoogle || []).push({}); \n<\/script>\n<\/div>\n\n\n\n<p>If we think about our normal every day numbering system, that is called &#8220;Decimal&#8221;, or Base 10. &nbsp; &nbsp;The only reason we are used to base 10 is because we have 10 fingers to count on. &nbsp; When the numbering systems were developed, humans became used to Base 10. &nbsp;There are 10 &#8220;symbols&#8221; available for counting (0 through 9). &nbsp;Remember that leading 0&#8217;s do not change the value of a number. &nbsp;01 is the exact same as 1. &nbsp; &nbsp;<\/p>\n\n\n\n<p>The least significant digit is on the right, because it has less impact on the overall value of the number. &nbsp; As our numbers get larger, we start adding digits to the right of that number. &nbsp;We can look at the value of 1000 and the value of 0001. &nbsp; In the number 1000, the value of 1 has more impact on the value than it does in the number 0001. &nbsp; &nbsp;As we add numbers to the left, those numbers become more significant.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Decimal breakdown<\/h2>\n\n\n\n<p>Before we understand binary, let&#8217;s take a look at this decimal number of 1000. &nbsp;We need to first change how you think about this number. &nbsp;Consider the following to understand how numbers are broken down before we try this on other numbering systems.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"> 10<sup>0<\/sup> = 1 &nbsp;(Any number to the power of 0 = 1)\n 10<sup>1<\/sup> = 10 &nbsp;(Any number to the power of 1 equals itself)\n 10<sup>2<\/sup> = 100 (10 x 10)\n 10<sup>3<\/sup> = 1000 (10 x 10 x 10)<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">Value:          10<sup>3<\/sup> 10<sup>2<\/sup> 10<sup>1<\/sup> 10<sup>0<\/sup>\nOriginal number: 1   0   0  0<\/pre>\n\n\n\n<p>Using the Example above, we can see that we have a &#8220;1&#8221; in the thousands place, so in decimal, we would calculate this as (1 x 1000) + (0 x 100) + (0 x 10) + (0 x 1). &nbsp; Of course our answer is 1000.<\/p>\n\n\n\n<p>Let&#8217;s try this with a different number, such as 2017:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">Value:          10<sup>3<\/sup> 10<sup>2<\/sup> 10<sup>1<\/sup> 10<sup>0<\/sup>\nOriginal number: 2   0   1  7<\/pre>\n\n\n\n<p>We would calculate this as (2 x 1000) + (0 x 100) + (1 x 10) + (7 x 1)&#8230; &nbsp; The answer is 2017.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Binary Breakdown<\/h2>\n\n\n\n<p>Now that you understand how this works in Decimal, let&#8217;s convert a binary number. &nbsp; Binary is a base 2 numbering system.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"> 2<sup>0<\/sup> = 1 &nbsp;(Any number to the power of 0 = 1)\n 2<sup>1<\/sup> = 10 &nbsp;(Any number to the power of 1 equals itself)\n 2<sup>2<\/sup> = 100 (2 x 2)\n 2<sup>3<\/sup> = 8(2 x 2 x 2)<\/pre>\n\n\n\n<pre class=\"wp-block-preformatted\">Value:           2<sup>3<\/sup>  2 <sup>2<\/sup> 2<sup>1<\/sup>  2<sup>0<\/sup>\nOriginal number: 1   0   0  0<\/pre>\n\n\n\n<p>Here we have (1 x 8) + (0 x 4) + (0 x 2) + (0 x 1) &nbsp;This number equals 8. &nbsp;Let&#8217;s try another one.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">Value:           2<sup>3<\/sup> 2 <sup>2<\/sup> 2<sup>1<\/sup> 2<sup>0<\/sup>\nOriginal number: 1  0  0  1<\/pre>\n\n\n\n<p>In this instance, we have (1 x 8) + (0 x 4) + (0 x 2) + (1 x 1) = 9<\/p>\n\n\n\n<p>Let&#8217;s look at this on a ControlLogix tag:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" width=\"630\" height=\"342\" data-src=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/07\/binary.png\" alt=\"Binary Conversion\" class=\"wp-image-1064 lazyload\" data-srcset=\"https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/07\/binary.png 630w, https:\/\/bryceautomation.com\/wp-content\/uploads\/2017\/07\/binary-300x163.png 300w\" data-sizes=\"(max-width: 630px) 100vw, 630px\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 630px; --smush-placeholder-aspect-ratio: 630\/342;\" \/><\/figure>\n<\/div>\n\n\n<p>Notice that &#8220;MyTag&#8221; is a Double Integer (DINT). &nbsp; A DINT consists of 32 bits (showing 16 here). &nbsp; We can look at this number as an Integer, or we can expand the tag to break it down into Binary. &nbsp; We see the value of 1001 in binary is the value of &#8220;9&#8221; in decimal. &nbsp;When we look at a tag, we need to ask ourselves what we want to look at. &nbsp; If we want to look at it as a number (such as a temperature), then we look at the number at the DINT level. &nbsp; If the tag is used for individual discrete (on\/off) devices, then we can expand the tag to see which individual bits are turned on.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Other Common Numbering Systems<\/h2>\n\n\n\n<p>Other common numbering systems include Hexadecimal\/BCD and Octal.  <\/p>\n\n\n\n<p>With Hex\/BCD, every 4 binary bits represent a hexadecimal number (0-F).  For example, the Binary 1111 0011 would be F3.  The hexadecimal numbering system works out very well for addressing in computers.  This is because computers usually have a word length in a multiple of 4 digits.  In Assembly language, we can easily specify memory locations with these hex digits.  This is easier to remember than a string of binary numbers.<\/p>\n\n\n\n<p>Similarly, Octal uses every 3 digits of binary code to represent an octal digit.  Octal was very common in older computers such as the Kenbak-1, the Altair 8800, and the PDP computers.  For example, 11 111 111 in binary would be the number 377 in octal.<\/p>\n\n\n\n<p>For more information, please visit the <a href=\"https:\/\/bryceautomation.com\/index.php\/category\/controllogix\/\">ControlLogix <\/a>category page!<\/p>\n\n\n\n<p>&#8212; Ricky Bryce<\/p>\n<div id=\"bryce-2566203117\" class=\"bryce-after-content bryce-entity-placement\"><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-8316758073402323\" crossorigin=\"anonymous\"><\/script><ins class=\"adsbygoogle\" style=\"display:block;\" data-ad-client=\"ca-pub-8316758073402323\" \ndata-ad-slot=\"4667596182\" \ndata-ad-format=\"auto\"><\/ins>\n<script> \n(adsbygoogle = window.adsbygoogle || []).push({}); \n<\/script>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Introduction to the Binary Numbering System Simply put, the Binary Numbering System is a base 2 numbering system. &nbsp; &nbsp;The only numbers available for use to count in binary are 1, and 0. &nbsp; You can think of this in many ways: &nbsp;True\/False, Yes\/No, or High\/Low. &nbsp; &nbsp;Computers work by using the Binary numbering system, <a class=\"moretag btn btn-primary\" href=\"https:\/\/bryceautomation.com\/index.php\/2017\/07\/10\/binary-numbering-system\/\">Read More \u00bb<\/a><\/p>\n","protected":false},"author":1,"featured_media":1064,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,8,4,3],"tags":[49,11],"class_list":{"0":"post-1061","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-arduino-other-microprocessors","8":"category-beginner","9":"category-controllogix","10":"category-information-technology","11":"tag-binary","12":"tag-controllogix","13":"czr-hentry"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Introduction to the Binary Numbering System (Base 2)<\/title>\n<meta name=\"description\" content=\"Introduction to the Binary Numbering System. 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