Octal to Binary

Octal to Binary

Octal uses base 8, so each digit represents one of eight values: 0 through 7. Binary uses base 2, so each octal digit can be replaced by a fixed 3-bit binary group.

Method

1. Split the octal number into digits.
2. Replace each digit with its 3-bit binary equivalent.
   • 0 → 000
   • 1 → 001
   • 2 → 010
   • 3 → 011
   • 4 → 100
   • 5 → 101
   • 6 → 110
   • 7 → 111
3. Join the groups together.
4. Simplify the result by removing any unnecessary leading zeros, but keep the value unchanged.

Example pattern

If a digit is 5, write 101. If a digit is 2, write 010. Putting the groups together gives the full binary number.

Check your work

• Every octal digit must become exactly 3 binary digits.
• The final binary number should represent the same value as the original octal number.
• If the answer begins with zeros, remove only the extra leading zeros, not the zeros inside the number.

This method is quick because it avoids converting through decimal.