To convert the octal number \( 562741_8 \) to binary, we first convert each octal digit to its 3-digit binary equivalent:

- \( 5_8 = 101_2 \)
- \( 6_8 = 110_2 \)
- \( 2_8 = 010_2 \)
- \( 7_8 = 111_2 \)
- \( 4_8 = 100_2 \)
- \( 1_8 = 001_2 \)

Now, we combine these binary groups to get the full binary number:

\[
562741_8 = 101 \, 110 \, 010 \, 111 \, 100 \, 001_2
\]

Thus, the binary equivalent of \( 562741_8 \) is:

\[
101110010111100001_2
\]

Do you want more details or have any questions?

Here are five questions that build on this concept:
1. How would you convert a base 2 number to base 8?
2. Can you convert \( 562741_8 \) directly to base 10?
3. What is the decimal value of the binary number \( 101110010111100001_2 \)?
4. How would you convert a base 16 number to binary?
5. What are the advantages of working in base 8 for computers?

**Tip:** Remember, each octal digit directly corresponds to three binary digits, making conversions between base 8 and base 2 straightforward.

Learn how to convert the octal number 562741 to binary using simple conversion techniques. This step-by-step guide explores how each digit in the base 8 number corresponds to a binary equivalent. Suitable for high school students in Grades 9-12.

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