Octal to Binary Converter

Table of Contents

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

How does octal to binary conversion work?

The conversion of an octal number to binary is based on the fact that each octal digit can be represented directly as a group of 3 binary bits. This is because the octal base (base 8) is a power of the binary base (base 2), allowing for a simple and direct conversion between these two number systems.

Octal to binary conversion method

There is no specific mathematical formula for converting octal to binary, as the conversion is performed by direct substitution. Each digit of the octal number is replaced by its 3-bit binary equivalent.

Conversion process

1. Take each digit of the octal number and convert it to its 3-bit binary equivalent.
2. Combine the 3-bit groups of each digit to form the complete binary number.
3. Omit leading zeros if necessary to get the most simplified binary result.

Example #1

Convert the octal number 57 to binary:

1. Take each digit and convert it to binary:
   • 5 in binary is 101
   • 7 in binary is 111
2. Combine the results:
   • The octal number 57 converts to 101111 in binary.

Result: 57 in octal is 101111 in binary.

Example #2

Convert the octal number 234 to binary:

1. Convert each digit to binary:
   • 2 in binary is 010
   • 3 in binary is 011
   • 4 in binary is 100
2. Combine the results:
   • The octal number 234 converts to 010011100 in binary.

Result: 234 in octal is 010011100 in binary.

Octal to binary conversion table