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State the octal equivalent of hexa decimal number (B34)16.
- a)(6454)8
- b)(4564)8
- c)(5464)8
- d)(5645)8
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
State the octal equivalent of hexa decimal number (B34)16.a)(6454)8b)(...
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.
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.
Calculation:
Hexadecimal to Octal Conversion:
Given, B3416 is a hexadecimal number.
B → 1011, 3 → 0011, 4 → 0100
1011 0011 0100
Now group them from right to left, each having 3 digits.
101, 100, 110, 100
101 → 5, 100 → 4, 110 → 6, 100 → 4
Hence, B3416 = 54648
Hexadecimal to Octal Conversion:
Given, B3416 is a hexadecimal number.
B → 1011, 3 → 0011, 4 → 0100
1011 0011 0100
Now group them from right to left, each having 3 digits.
101, 100, 110, 100
101 → 5, 100 → 4, 110 → 6, 100 → 4
Hence, B3416 = 54648
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Community Answer
State the octal equivalent of hexa decimal number (B34)16.a)(6454)8b)(...
To find the octal equivalent of a hexadecimal number, we need to convert each hexadecimal digit into its binary equivalent and then group the binary digits into groups of three from right to left. Each group of three binary digits can then be converted into its octal equivalent.
Given hexadecimal number: (B34)16
1. Convert hexadecimal digits to binary:
B = 1011
3 = 0011
4 = 0100
2. Group binary digits into groups of three:
1011 0011 0100
3. Convert each group of three binary digits to octal:
1011 = 13
0011 = 3
0100 = 4
4. Combine the octal digits:
(13 3 4)8
Therefore, the octal equivalent of the hexadecimal number (B34)16 is (134)8.
Let's analyze each option provided:
a) (6454)8: This is already in octal form and not the octal equivalent of (B34)16.
b) (4564)8: This is already in octal form and not the octal equivalent of (B34)16.
c) (5464)8: This is the octal equivalent of (B34)16 as determined above.
d) (5645)8: This is already in octal form and not the octal equivalent of (B34)16.
Therefore, the correct answer is option 'C', (5464)8.
Given hexadecimal number: (B34)16
1. Convert hexadecimal digits to binary:
B = 1011
3 = 0011
4 = 0100
2. Group binary digits into groups of three:
1011 0011 0100
3. Convert each group of three binary digits to octal:
1011 = 13
0011 = 3
0100 = 4
4. Combine the octal digits:
(13 3 4)8
Therefore, the octal equivalent of the hexadecimal number (B34)16 is (134)8.
Let's analyze each option provided:
a) (6454)8: This is already in octal form and not the octal equivalent of (B34)16.
b) (4564)8: This is already in octal form and not the octal equivalent of (B34)16.
c) (5464)8: This is the octal equivalent of (B34)16 as determined above.
d) (5645)8: This is already in octal form and not the octal equivalent of (B34)16.
Therefore, the correct answer is option 'C', (5464)8.
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