A binary number 1101110111 is separated into three-digit groupings by starting at the right end of the number and supplying leading zeros at the left if necessary: 001 101 110 111. The binary groups are then replaced by their octal equivalents:
001two	 = 	1eight	    	101two	 = 	5eight
110two	 = 	6eight	    	111two	 = 	7eight
and the binary number is converted to its octal equivalent: 1567. Conversely, an octal number can be expanded to a binary number using the same table of equivalents:
5307eight = 101 011 000 111two.

Convert the number to the octal system.
111 111 011 011 100 110two

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!

A binary number 1101110111 is separated into three-digit groupings by starting at the right end of the number and supplying leading zeros at the left if necessary: 001 101 110 111. The binary groups are then replaced by their octal equivalents: 001two = 1eight 101two = 5eight 110two = 6eight 111two = 7eight and the binary number is converted to its octal equivalent: 1567. Conversely, an octal number can be expanded to a binary number using the same table of equivalents: 5307eight = 101 011 000 111two. Convert the number to the octal system. 111 111 011 011 100 110two

Learn how to convert the binary number 111111011011100110two into its octal equivalent step-by-step. This problem covers key number system concepts, including binary to octal conversion techniques and grouping theorems. Suitable for students in Grades 8-10.

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