Question
Download Solution PDFGiven below are two statements:
Statement I: (67)10 = (10100111)2
Statement II: (11010110)2 = (214)10
In the light of the above statements. choose the correct answer from the options given below
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFStatement I: (67)10 = (10100111)2, this statement is false
(67)10 = (1000011)2
Step-by-step solution
Step 1: Divide (67)10 successively by 2 until the quotient is 0:
- 67/2 = 33, remainder is 1
- 33/2 = 16, remainder is 1
- 16/2 = 8, remainder is 0
- 8/2 = 4, remainder is 0
- 4/2 = 2, remainder is 0
- 2/2 = 1, remainder is 0
- 1/2 = 0, remainder is 1
Step 2: Read from the bottom (MSB) to the top (LSB) as 1000011.
Statement II: (11010110)2 = (214)10
- Statement II is also true because the binary representation of 214 is 11010110. This can be verified by converting 214 to binary using the same steps as above.
Therefore, statement I is false but Statement II is true.
Last updated on Jun 11, 2025
-> The UGC NET Exam Schedule 2025 for June has been released on its official website.
-> Check UPSC Prelims Result 2025, UPSC IFS Result 2025, UPSC Prelims Cutoff 2025, UPSC Prelims Result 2025 Name Wise & Rollno. Wise
-> The UGC NET Application Correction Window 2025 is available from 14th May to 15th May 2025.
-> The UGC NET 2025 online application form submission closed on 12th May 2025.
-> The June 2025 Exam will be conducted from 21st June to 30th June 2025
-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.
-> The exam is conducted bi-annually - in June and December cycles.
-> The exam comprises two papers - Paper I and Paper II. Paper I consists of 50 questions and Paper II consists of 100 questions.
-> The candidates who are preparing for the exam can check the UGC NET Previous Year Papers and UGC NET Test Series to boost their preparations.