What is the octal system?
The octal number system is a base-8 system. It uses only eight digits: 0 1 2 3 4 5 6 7. There is no digit 8 or 9. Each position has a place value that is a power of 8 — reading from right to left these are 1, 8, 64, 512, and so on.
Key idea
To turn octal into decimal, multiply each digit by its place value (a power of 8) and add the results. From right to left the place values are 1, 8 and 64.
Converting between bases
To change octal to decimal, expand each digit. For example, octal 17 means (1 × 8) + (7 × 1) = 8 + 7 = 15 in decimal. To go the other way, divide the decimal number by 8 over and over and read the remainders from bottom to top.
Octal is closely linked to binary because 8 = 2 × 2 × 2. This means every single octal digit maps exactly to a group of three binary bits. So binary 111 is octal 7, and binary 001 000 is octal 10.
Example
Convert binary 101010 to octal. Split into threes from the right: 101 and 010. That is 5 and 2, so the answer is octal 52.
Why we use it
Long binary numbers are hard for people to read without slips. Octal shrinks them to a third of the length while keeping an easy link back to binary, which is why early computer systems often used it.