Question
Download Solution PDFWhich of the following is the correct octal representation of the hexadecimal number 1A3?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Hexadecimal to Octal Conversion
Definition: Hexadecimal and octal are both positional numeral systems, widely used in computing and digital electronics. Hexadecimal (base-16) uses sixteen symbols, 0-9 and A-F, to represent values, while octal (base-8) uses eight symbols, 0-7.
To convert a hexadecimal number to its octal equivalent, it is often easiest to first convert it to binary (base-2), and then from binary to octal. This method works because both octal and hexadecimal are powers of 2 (octal is 23 and hexadecimal is 24).
Step-by-Step Solution:
Given hexadecimal number: 1A3
1. Convert Hexadecimal to Binary:
Each hexadecimal digit can be represented by a 4-bit binary number:
- 1 (Hex) = 0001 (Binary)
- A (Hex) = 1010 (Binary)
- 3 (Hex) = 0011 (Binary)
So, the hexadecimal number 1A3 can be written in binary as: 0001 1010 0011
2. Group Binary Digits into Sets of Three:
Since octal is base-8 and each octal digit corresponds to 3 binary digits, we group the binary digits in sets of three, starting from the right:
- 0001 1010 0011 (Binary)
- 000 110 100 011 (Binary, grouped in sets of three)
3. Convert Binary Sets to Octal:
Each group of three binary digits can be converted directly to its octal equivalent:
- 000 (Binary) = 0 (Octal)
- 110 (Binary) = 6 (Octal)
- 100 (Binary) = 4 (Octal)
- 011 (Binary) = 3 (Octal)
So, the binary number 000 110 100 011 can be written in octal as: 0643
Hence, the correct octal representation of the hexadecimal number 1A3 is 643.
Important Information:
To analyze other options, let's convert the hexadecimal number 1A3 using the same method:
- Option 1: 346
- 346 (Octal) in binary: 011 100 110
- Groups: 011 100 110 (Binary) = 3 4 6 (Octal)
- Binary to Hexadecimal: 011100110 (Binary) = 1C6 (Hex)
- 1C6 ≠ 1A3
- Option 2: 124
- 124 (Octal) in binary: 001 010 100
- Groups: 001 010 100 (Binary) = 1 2 4 (Octal)
- Binary to Hexadecimal: 001010100 (Binary) = 54 (Hex)
- 54 ≠ 1A3
- Option 3: 634
- 634 (Octal) in binary: 110 011 100
- Groups: 110 011 100 (Binary) = 6 3 4 (Octal)
- Binary to Hexadecimal: 110011100 (Binary) = 19C (Hex)
- 19C ≠ 1A3
Therefore, the correct option is confirmed as option 4: 643.
Last updated on Jun 7, 2025
-> RRB JE CBT 2 answer key 2025 for June 4 exam has been released at the official website.
-> Check Your Marks via RRB JE CBT 2 Rank Calculator 2025
-> RRB JE CBT 2 admit card 2025 has been released.
-> RRB JE CBT 2 city intimation slip 2025 for June 4 exam has been released at the official website.
-> RRB JE CBT 2 Cancelled Shift Exam 2025 will be conducted on June 4, 2025 in offline mode.
-> RRB JE CBT 2 Exam Analysis 2025 is Out, Candidates analysis their exam according to Shift 1 and 2 Questions and Answers.
-> The RRB JE Notification 2024 was released for 7951 vacancies for various posts of Junior Engineer, Depot Material Superintendent, Chemical & Metallurgical Assistant, Chemical Supervisor (Research) and Metallurgical Supervisor (Research).
-> The selection process includes CBT 1, CBT 2, and Document Verification & Medical Test.
-> The candidates who will be selected will get an approximate salary range between Rs. 13,500 to Rs. 38,425.
-> Attempt RRB JE Free Current Affairs Mock Test here
-> Enhance your preparation with the RRB JE Previous Year Papers.