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.