{"id":26964,"date":"2025-06-19T19:57:53","date_gmt":"2025-06-19T19:57:53","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26964"},"modified":"2025-06-19T19:58:00","modified_gmt":"2025-06-19T19:58:00","slug":"convert-the-following-binary-numbers-into-decimal-numbers","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/convert-the-following-binary-numbers-into-decimal-numbers\/","title":{"rendered":"Convert the following Binary numbers into Decimal numbers"},"content":{"rendered":"\n<p>Convert the following Binary numbers into Decimal numbers.a. 10101<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Correct Answer:<\/h3>\n\n\n\n<p><strong>Binary 10101 = Decimal 21<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 Step-by-Step Explanation:<\/h3>\n\n\n\n<p>Binary numbers are based on the <strong>base-2<\/strong> numeral system, which uses only two digits: <strong>0<\/strong> and <strong>1<\/strong>. Each digit (called a <strong>bit<\/strong>) represents an increasing power of 2, starting from the <strong>rightmost digit (least significant bit)<\/strong>.<\/p>\n\n\n\n<p>To convert binary <strong>10101<\/strong> to decimal:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Write the binary number with positional powers of 2:<\/h4>\n\n\n\n<pre class=\"wp-block-code\"><code>Binary:     1   0   1   0   1\nPosition:   4   3   2   1   0  \u2192 (these are the exponents for base 2)\n<\/code><\/pre>\n\n\n\n<p>Now calculate the <strong>value of each bit<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\u00d724=161 \u00d7 2^4 = 16<\/li>\n\n\n\n<li>0\u00d723=00 \u00d7 2^3 = 0<\/li>\n\n\n\n<li>1\u00d722=41 \u00d7 2^2 = 4<\/li>\n\n\n\n<li>0\u00d721=00 \u00d7 2^1 = 0<\/li>\n\n\n\n<li>1\u00d720=11 \u00d7 2^0 = 1<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Add them all up:<\/h4>\n\n\n\n<p>16+0+4+0+1=2116 + 0 + 4 + 0 + 1 = \\boxed{21}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 Why This Works:<\/h3>\n\n\n\n<p>The decimal system (base-10) is what we use in everyday life. The binary system (base-2) is used by computers and digital systems because it\u2019s simple and efficient for representing <strong>on\/off<\/strong> states with <strong>1s and 0s<\/strong>.<\/p>\n\n\n\n<p>Each digit in a binary number represents <strong>an increasing power of 2<\/strong> from right to left. The digit tells us whether that power of 2 should be <strong>included (1)<\/strong> or <strong>ignored (0)<\/strong>.<\/p>\n\n\n\n<p>So in <strong>10101<\/strong>, we\u2019re including:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>24=162^4 = 16,<\/li>\n\n\n\n<li>22=42^2 = 4,<\/li>\n\n\n\n<li>20=12^0 = 1,<\/li>\n<\/ul>\n\n\n\n<p>Which totals to <strong>21<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer:<\/h3>\n\n\n\n<p><strong>Binary 10101 = Decimal 21<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert the following Binary numbers into Decimal numbers.a. 10101 The correct answer and explanation is: \u2705 Correct Answer: Binary 10101 = Decimal 21 \ud83e\udde0 Step-by-Step Explanation: Binary numbers are based on the base-2 numeral system, which uses only two digits: 0 and 1. Each digit (called a bit) represents an increasing power of 2, starting [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26964","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26964","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26964"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26964\/revisions"}],"predecessor-version":[{"id":26965,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26964\/revisions\/26965"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26964"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}