Binary to Octal Converter

Table of Contents

• How does binary to octal conversion work?
• Binary to octal conversion method
• Conversion process
• Example 1
• Example 2
• Binary to octal conversion table

How does binary to octal conversion work?

The conversion of a binary number to octal is a straightforward process due to the direct relationship between these two number systems. Since the binary system (base 2) and the octal system (base 8) are related by powers of 2, a binary number can be divided into groups of 3 bits, each of which can be directly converted to an octal digit.

Binary to octal conversion method

There is no complex mathematical formula for binary to octal conversion, as it is based on dividing the binary number into groups of 3 bits and converting each group to its corresponding octal value.

Conversion process

1. Divide the binary number into groups of 3 bits, starting from the right. If the number of bits is not a multiple of 3, add zeros to the left to complete the last group.
2. Convert each group of 3 bits to its decimal equivalent, which represents a digit in the octal system.
3. Combine the obtained digits to form the final octal number.

Example 1

Convert the binary number 101110 to octal:

1. Divide into groups of 3 bits:
   • 101 and 110
2. Convert each group to decimal:
   • 101 in decimal is 5
   • 110 in decimal is 6
3. Combine the results:
   • The binary number 101110 converts to 56 in octal.

Result: 101110 in binary is 56 in octal.

Example 2

Convert the binary number 1001011 to octal:

1. Divide into groups of 3 bits (add a 0 at the start to complete):
   • 010, 010, and 011
2. Convert each group to decimal:
   • 010 in decimal is 2
   • 010 in decimal is 2
   • 011 in decimal is 3
3. Combine the results:
   • The binary number 1001011 converts to 223 in octal.

Result: 1001011 in binary is 223 in octal.

Binary to octal conversion table