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Find the Octal equivalent of hexa decimal number (FB2)16?
- a)(7652)8
- b)(7662)8
- c)(7654)8
- d)(7658)8
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Find the Octal equivalent of hexa decimal number (FB2)16?a)(7652)8b)(7...
Concept:
A number system includes the number of independent digits used in the number system (the base), the place values of the different digits constituting the number, and the maximum numbers that can be written with the given number of digits.
Octal numbers: These numbers use digits from 0 to 7, total of 8 digits, and hence they are called octal number system. Octal numbers have base 8.
Hexadecimal numbers: The numbers which have base 16. It uses 16 different digits to represent the numbers. It is denoted as h16, where h is a hexadecimal number. It may be a combination of alphabets and numbers. Thus, it includes numbers from 0 to 9 and alphabets A to F.
Octal numbers: These numbers use digits from 0 to 7, total of 8 digits, and hence they are called octal number system. Octal numbers have base 8.
Hexadecimal numbers: The numbers which have base 16. It uses 16 different digits to represent the numbers. It is denoted as h16, where h is a hexadecimal number. It may be a combination of alphabets and numbers. Thus, it includes numbers from 0 to 9 and alphabets A to F.
Calculation:
Hexadecimal to Octal Conversion:
Given, (FB2)16 is a hexadecimal number.
F → 1111, B → 1011, 2 → 0010 1111 1011 0010
Now group them from right to left, each having 3 digits.
111, 110, 110, 010
111 → 7, 110 → 6, 110 → 6, 010 → 2
Hence, FB216 = 76628
Hexadecimal to Octal Conversion:
Given, (FB2)16 is a hexadecimal number.
F → 1111, B → 1011, 2 → 0010 1111 1011 0010
Now group them from right to left, each having 3 digits.
111, 110, 110, 010
111 → 7, 110 → 6, 110 → 6, 010 → 2
Hence, FB216 = 76628
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Find the Octal equivalent of hexa decimal number (FB2)16?a)(7652)8b)(7...
Octal Equivalent of Hexadecimal Number (FB2)16
To find the octal equivalent of a hexadecimal number, we need to convert each hexadecimal digit into its equivalent binary representation and then group the binary digits into groups of three from right to left. Finally, we convert each group of three binary digits into its equivalent octal digit.
Step 1: Convert Hexadecimal to Binary
To convert the hexadecimal number (FB2)16 to binary, we can use the following table:
So, (FB2)16 in binary is 111110110010.
Step 2: Group Binary Digits
Starting from the right, group the binary digits into groups of three:
1 111 101 100 10
Step 3: Convert Binary to Octal
Now, we convert each group of three binary digits into its equivalent octal digit:
1 7 5 4 2
Therefore, the octal equivalent of (FB2)16 is (17542)8.
Conclusion
The correct answer is option 'B' (7662)8.
To find the octal equivalent of a hexadecimal number, we need to convert each hexadecimal digit into its equivalent binary representation and then group the binary digits into groups of three from right to left. Finally, we convert each group of three binary digits into its equivalent octal digit.
Step 1: Convert Hexadecimal to Binary
To convert the hexadecimal number (FB2)16 to binary, we can use the following table:
| Hexadecimal | Binary |
|---|---|
| F | 1111 |
| B | 1011 |
| 2 | 0010 |
So, (FB2)16 in binary is 111110110010.
Step 2: Group Binary Digits
Starting from the right, group the binary digits into groups of three:
1 111 101 100 10
Step 3: Convert Binary to Octal
Now, we convert each group of three binary digits into its equivalent octal digit:
1 7 5 4 2
Therefore, the octal equivalent of (FB2)16 is (17542)8.
Conclusion
The correct answer is option 'B' (7662)8.
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