Binary to Octal

Binary to Octal: Method

Binary and octal are both place-value systems, so the easiest conversion is to regroup the binary digits into sets of three, starting from the right. Each 3-bit group corresponds to one octal digit.

Steps

1. Write the binary number clearly.
2. Group bits in threes from the right. If the leftmost group has fewer than 3 bits, add leading zeros to complete it.
3. Convert each 3-bit group to one octal digit. Use the pattern:
   • 000 = 0, 001 = 1, 010 = 2, 011 = 3
   • 100 = 4, 101 = 5, 110 = 6, 111 = 7
4. Combine the octal digits in the same order as the groups.

Example check

Binary 101101 becomes 101 101, so the octal digits are 5 5, giving 55.

Quick check

If you want to verify your answer, convert the octal result back to binary by replacing each octal digit with its 3-bit binary group. If it matches the original number, your conversion is correct.

Common mistake

Do not group bits in fours or twos. Octal is based on groups of three, so that is the key idea to remember.