What is 1010111100 binary to octal?

The binary number 1010111100 converts to the octal number 1274.

Understanding Binary to Octal Conversion

Converting a binary number to an octal number is a straightforward process that leverages the relationship between the two bases. Octal (base-8) numbers use digits from 0 to 7, while binary (base-2) numbers use only 0 and 1. The key to this conversion lies in the fact that 8 is a power of 2 (specifically, 2^3). This means that every three binary digits correspond to exactly one octal digit.

Step-by-Step Conversion of 1010111100₂ to Octal

To convert the binary number 1010111100 to its octal equivalent, we follow these steps:

1. Group Binary Digits: Begin by grouping the binary digits into sets of three, starting from the rightmost digit. If the leftmost group has fewer than three digits, add leading zeros to complete the group.

   • Original binary: 1010111100
   • Grouping: 1 010 111 100
   • Adding leading zeros to the leftmost group (if needed): 001 010 111 100

2. Convert Each Group to Octal: Convert each three-digit binary group into its corresponding single octal digit. Each binary group represents a value from 0 to 7.

   • 000₂ = 0₈
   • 001₂ = 1₈
   • 010₂ = 2₈
   • 011₂ = 3₈
   • 100₂ = 4₈
   • 101₂ = 5₈
   • 110₂ = 6₈
   • 111₂ = 7₈

   Let's apply this to our grouped binary number:

   Binary Group	Octal Equivalent
   001	1
   010	2
   111	7
   100	4

3. Combine Octal Digits: Finally, combine the resulting octal digits in the same order to form the complete octal number.

   Combining 1, 2, 7, and 4 gives us 1274.

Therefore, 1010111100 binary is equal to 1274 octal. This method of grouping binary numbers into sets of three is the standard approach for converting binary to octal.