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Convert the binary number 10101110 to octal.
- a)128
- b)184
- c)256
- d)312
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Convert the binary number 10101110 to octal.a)128b)184c)256d)312Correc...
Concept:
There are only 8 digits (from 0 to 7) in the octal number system, so we can represent any digit of octal number system using only 3 bits as following below:
Follow below-mentioned steps to convert from Binary to Octal:
Step I: Select Binary Number.
Step II: Divide the binary digits into a group of three (starting from right) for the Integer part and start from left for the Fraction part.
Step III: Convert each group of three binary digits into an octal digit referring to the above table.
Follow below-mentioned steps to convert from Binary to Octal:
Step I: Select Binary Number.
Step II: Divide the binary digits into a group of three (starting from right) for the Integer part and start from left for the Fraction part.
Step III: Convert each group of three binary digits into an octal digit referring to the above table.
Calculation
Step I: Binary Number: 110101110
Step II: Divide the binary digits into the group of three (starting from the right) for the Integer part:
(010 101 110)
Step III: Convert each group of three binary digits into an octal digit referring to the above table:
Step I: Binary Number: 110101110
Step II: Divide the binary digits into the group of three (starting from the right) for the Integer part:
(010 101 110)
Step III: Convert each group of three binary digits into an octal digit referring to the above table:
(010 101 110)2 = (256)8
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Convert the binary number 10101110 to octal.a)128b)184c)256d)312Correc...
Understanding Binary to Octal Conversion
To convert the binary number 10101110 to octal, follow these steps:
Step 1: Group the Binary Digits
- Start from the right and group the binary digits into sets of three.
- If necessary, add leading zeros to the leftmost group to make it a full set of three.
For 10101110, we group it as follows:
- 010 101 110
Step 2: Convert Each Group to Decimal
- Now, convert each group of three binary digits to its octal equivalent.
- 010 in binary = 2 in decimal
- 101 in binary = 5 in decimal
- 110 in binary = 6 in decimal
Step 3: Combine the Octal Digits
- Combine the decimal values obtained from each group to form the final octal number.
- Therefore, the octal representation is 256.
Final Result
- The octal equivalent of the binary number 10101110 is 256.
Conclusion
- The correct answer for the conversion of the binary number 10101110 to octal is option 'C' - 256.
To convert the binary number 10101110 to octal, follow these steps:
Step 1: Group the Binary Digits
- Start from the right and group the binary digits into sets of three.
- If necessary, add leading zeros to the leftmost group to make it a full set of three.
For 10101110, we group it as follows:
- 010 101 110
Step 2: Convert Each Group to Decimal
- Now, convert each group of three binary digits to its octal equivalent.
- 010 in binary = 2 in decimal
- 101 in binary = 5 in decimal
- 110 in binary = 6 in decimal
Step 3: Combine the Octal Digits
- Combine the decimal values obtained from each group to form the final octal number.
- Therefore, the octal representation is 256.
Final Result
- The octal equivalent of the binary number 10101110 is 256.
Conclusion
- The correct answer for the conversion of the binary number 10101110 to octal is option 'C' - 256.
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