Octal to Decimal

Octal to Decimal

Octal uses base 8, so each digit represents a power of 8. To convert an octal number to decimal, expand it by place value and add the results.

Method

1. Write the digits from left to right.
2. Assign powers of 8 starting with the rightmost digit: (8^0, 8^1, 8^2,\dots)
3. Multiply each digit by its matching power of 8.
4. Add all the products to get the decimal value.

For example, an octal number with digits (a,b,c) becomes: [ a\cdot 8^2 + b\cdot 8^1 + c\cdot 8^0 ]

Useful check

• Make sure every digit is between 0 and 7.
• Recompute carefully if the number has several digits, since the powers of 8 grow quickly.
• You can check your result by seeing whether the expanded sum matches the original octal digits.

Tip

If the number has a trailing zero, the decimal result is still found the same way; the zero simply contributes nothing to the sum. Always simplify the final answer to a single decimal number.