Let's convert the binary number $111 \ 111 \ 011 \ 011 \ 100 \ 110_2$ to the octal system by grouping the binary digits into sets of three and then converting each set into its octal equivalent.

Step 1: Group the binary digits into sets of three from right to left:

• $111_2$
• $111_2$
• $011_2$
• $011_2$
• $100_2$
• $110_2$

Step 2: Convert each group to its octal equivalent:

• $111_2 = 7_8$
• $111_2 = 7_8$
• $011_2 = 3_8$
• $011_2 = 3_8$
• $100_2 = 4_8$
• $110_2 = 6_8$

Step 3: Write the octal digits together:

The octal number is $773346_8$.

Thus, $111 \ 111 \ 011 \ 011 \ 100 \ 110_2$ in binary is equal to $773346_8$ in octal.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you convert binary numbers with fractional parts into octal?
2. What is the octal equivalent of the binary number $110011011011_2$?
3. How would you convert an octal number back into binary?
4. Why does grouping binary digits into sets of three help with octal conversion?
5. How does octal relate to hexadecimal conversions?

Tip: When converting binary to octal, always group binary digits in threes starting from the right. Add leading zeros if needed!