Convert the number to the octal system.
111 111 011 011 011 100two

Let's convert the binary number \( 111\ 111\ 011\ 011\ 011\ 100_2 \) into its octal equivalent.

### Step-by-Step Process:
1. **Group the binary digits** into groups of three, starting from the right. If necessary, pad the leftmost group with zeros:
   \[
   111\ 111\ 011\ 011\ 011\ 100_2
   \]
   The groupings will be:
   \[
   111\ 111\ 011\ 011\ 011\ 100_2 \Rightarrow 111\ | \ 111\ | \ 011\ | \ 011\ | \ 011\ | \ 100
   \]
2. **Convert each group of three binary digits** into its octal equivalent:

   - \( 111_2 = 7_8 \)
   - \( 111_2 = 7_8 \)
   - \( 011_2 = 3_8 \)
   - \( 011_2 = 3_8 \)
   - \( 011_2 = 3_8 \)
   - \( 100_2 = 4_8 \)

3. **Write down the octal digits** in the same order:
   \[
   777334_8
   \]

Thus, the binary number \( 111\ 111\ 011\ 011\ 011\ 100_2 \) is equivalent to \( 777334_8 \) in the octal system.

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Would you like more details or have any questions?

Here are some related questions:
1. How do you convert from octal to binary?
2. What is the significance of octal numbers in computer systems?
3. How do you convert binary numbers to hexadecimal?
4. Can you explain how binary grouping affects conversions?
5. What are the applications of different number systems like octal and hexadecimal?

**Tip**: Always group binary digits in threes for octal conversions and in fours for hexadecimal conversions!

Convert the number to the octal system. 111 111 011 011 011 100two

Learn how to convert the binary number 111 111 011 011 011 100 to the octal system using binary grouping and conversion rules. This guide covers key concepts in number systems and is suitable for students in Grades 6-8.

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