{"id":26757,"date":"2025-06-19T18:10:46","date_gmt":"2025-06-19T18:10:46","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26757"},"modified":"2025-06-19T18:10:47","modified_gmt":"2025-06-19T18:10:47","slug":"the-binary-number-10101-is-equivalent-to-decimal-number","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-binary-number-10101-is-equivalent-to-decimal-number\/","title":{"rendered":"The binary number 10101 is equivalent to decimal number"},"content":{"rendered":"\n

‘The binary number 10101 is equivalent to decimal number Select one: a. 19 b. 21 c; 27 d. 12’<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

Correct Answer: b. 21<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation (300 words):<\/strong><\/h3>\n\n\n\n

Binary numbers are a base-2 numeral system, meaning they use only two digits: 0 and 1<\/strong>. Each digit in a binary number represents a power of 2, starting from the rightmost digit (which is 202^0).<\/p>\n\n\n\n

Let\u2019s break down the binary number 10101<\/strong>:<\/p>\n\n\n\n

We label each digit with its corresponding power of 2 position:<\/p>\n\n\n\n

Binary:     1   0   1   0   1\nPosition:   4   3   2   1   0 (right to left)\nPower of 2: 2\u2074 2\u00b3 2\u00b2 2\u00b9 2\u2070\n<\/code><\/pre>\n\n\n\n
Now, multiply each digit by its corresponding power of 2:<\/p>\n\n\n\n
    \n
  • 1\u00d724=1\u00d716=161 \\times 2^4 = 1 \\times 16 = 16<\/li>\n\n\n\n
  • 0\u00d723=0\u00d78=00 \\times 2^3 = 0 \\times 8 = 0<\/li>\n\n\n\n
  • 1\u00d722=1\u00d74=41 \\times 2^2 = 1 \\times 4 = 4<\/li>\n\n\n\n
  • 0\u00d721=0\u00d72=00 \\times 2^1 = 0 \\times 2 = 0<\/li>\n\n\n\n
  • 1\u00d720=1\u00d71=11 \\times 2^0 = 1 \\times 1 = 1<\/li>\n<\/ul>\n\n\n\n
    Add up the results: 16+0+4+0+1=2116 + 0 + 4 + 0 + 1 = \\boxed{21}<\/p>\n\n\n\n
    So, the binary number 10101<\/strong> is equivalent to the decimal number 21<\/strong>.<\/p>\n\n\n\n
    \n\n\n\n
    Why This Matters:<\/strong><\/h3>\n\n\n\n
    Understanding how to convert binary to decimal is essential in computer science and digital electronics because computers operate using binary logic. Every number, letter, or instruction a computer processes is ultimately translated into binary. Learning to convert between binary and decimal helps build a foundation for more advanced concepts like programming, data encoding, and computer architecture.<\/p>\n\n\n\n
    This kind of problem also enhances logical thinking and numeracy, especially in contexts where low-level computation is relevant\u2014like network protocols, memory addressing, or hardware design.<\/p>\n\n\n\n
    So, 10101\u2082 = 21\u2081\u2080<\/strong>, and the correct answer is (b) 21<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"
    ‘The binary number 10101 is equivalent to decimal number Select one: a. 19 b. 21 c; 27 d. 12’ The correct answer and explanation is: Correct Answer: b. 21 Explanation (300 words): Binary numbers are a base-2 numeral system, meaning they use only two digits: 0 and 1. Each digit in a binary number represents […]<\/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-26757","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26757","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=26757"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26757\/revisions"}],"predecessor-version":[{"id":26758,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26757\/revisions\/26758"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26757"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26757"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26757"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}