Convert F6F16 to octal. F6F 16 =
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Convert F6F_16 to octal.
![**Hexadecimal to Octal Conversion**
To convert the hexadecimal number \( F6F_{16} \) to octal, follow these steps:
1. First, convert the hexadecimal value to its binary equivalent.
2. Then, convert the binary representation to its octal form.
**Example Problem:**
Convert \( F6F_{16} \) to octal.
**Step-by-Step Solution:**
1. Write the hexadecimal number \( F6F_{16} \).
2. Convert each hexadecimal digit to its 4-bit binary equivalent:
- \( F = 1111 \)
- \( 6 = 0110 \)
- \( F = 1111 \)
So, \( F6F_{16} \) in binary is:
\( 1111 \ 0110 \ 1111 \)
3. Group the binary digits into sets of three, starting from the right (add leading zeros if necessary):
\( 111 \ 101 \ 101 \ 111 \)
4. Convert each group of three binary digits to its octal equivalent:
- \( 111 \rightarrow 7 \)
- \( 101 \rightarrow 5 \)
- \( 101 \rightarrow 5 \)
- \( 111 \rightarrow 7 \)
Therefore, \( 1111 \ 0110 \ 1111_2 = 7557_8 \).
**Final Answer:**
\[ F6F_{16} = 7557_8 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F105fff1d-4db1-4cc6-9fff-4ea0e94f4214%2F174cb08a-e18c-43fc-82c5-40a783e54607%2F8fzt1f_processed.png&w=3840&q=75)
Transcribed Image Text:**Hexadecimal to Octal Conversion**
To convert the hexadecimal number \( F6F_{16} \) to octal, follow these steps:
1. First, convert the hexadecimal value to its binary equivalent.
2. Then, convert the binary representation to its octal form.
**Example Problem:**
Convert \( F6F_{16} \) to octal.
**Step-by-Step Solution:**
1. Write the hexadecimal number \( F6F_{16} \).
2. Convert each hexadecimal digit to its 4-bit binary equivalent:
- \( F = 1111 \)
- \( 6 = 0110 \)
- \( F = 1111 \)
So, \( F6F_{16} \) in binary is:
\( 1111 \ 0110 \ 1111 \)
3. Group the binary digits into sets of three, starting from the right (add leading zeros if necessary):
\( 111 \ 101 \ 101 \ 111 \)
4. Convert each group of three binary digits to its octal equivalent:
- \( 111 \rightarrow 7 \)
- \( 101 \rightarrow 5 \)
- \( 101 \rightarrow 5 \)
- \( 111 \rightarrow 7 \)
Therefore, \( 1111 \ 0110 \ 1111_2 = 7557_8 \).
**Final Answer:**
\[ F6F_{16} = 7557_8 \]
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