What is the octal representation of the binary number 100101111?
Understand the Problem
The question is asking for the conversion of a binary number (100101111) into its octal representation. The binary number is provided in a spaced format, and we need to first combine the digits and then convert it to octal.
Answer
$1317_8$
Answer for screen readers
The octal representation of the binary number $100101111$ is $1317_{8}$.
Steps to Solve
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Combine the binary digits First, we will combine the binary digits from the spaced format to form a single binary number: $$ 100101111 $$
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Group binary digits into sets of three from the right To convert binary to octal, we need to group the binary digits into sets of three. Starting from the right, we will group the digits as follows: $$ (1)(001)(011)(111) $$
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Convert each group to octal Now, we convert each group of three binary digits to their corresponding octal values:
- $111$ in binary is $7$ in octal
- $011$ in binary is $3$ in octal
- $001$ in binary is $1$ in octal
- $1$ (which can be thought as $001$) in binary is $1$ in octal
So, we have: $$ 100101111_{2} = (1)(001)(011)(111){2} = 1317{8} $$
- Combine the octal digits Finally, we combine the octal digits we found: Thus, the octal representation is: $$ 1317_{8} $$
The octal representation of the binary number $100101111$ is $1317_{8}$.
More Information
Converting between number systems is a useful skill in computer science and digital electronics. Octal numbers are base-8 and are often used in programming and data representation. Each digit in the octal system represents three binary digits.
Tips
- Forgetting to group the binary digits correctly (do not overlook leading zeros).
- Incorrect conversion of binary groups to octal values. Always double-check your binary-to-octal conversions.
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