Octal to Decimal Converter

What Is the Octal Number System?

The octal number system uses base 8 and only digits 0 through 7. Each digit has a place value based on a power of 8. Positional notation shows each digit's value. This system gives students a simple way to group binary digits.

What Is the Decimal Number System?

The decimal number system uses base 10 and digits 0 through 9. Each digit has a place value based on a power of 10. We use decimal values for everyday math. The same place value idea helps explain octal conversion and number reading.

How to Convert Octal to Decimal Manually

To convert an octal number, multiply each digit by its matching power of 8, then add the products.

Formula: Powers of 8

$Decimal = d_n×8^n + ... + d_1×8^1 + d_0×8^0$

Step by step Guide: Octal Conversion

1. Write the octal number.
2. Start with $8^0$ on the right.
3. Increase the power by one moving left.
4. Multiply each digit by its power.
5. Add the products.

Practical Example: Octal to Decimal

Convert $157_8$.

1. $1×8^2 + 5×8^1 + 7×8^0$
2. $64 + 40 + 7$
3. $111_{10}$

So, $157_8 = 111_{10}$.

This method works because each position has a value based on a power of 8.

Octal to Decimal Conversion Table

Note: Each row shows a common octal value and its matching decimal value. Use the table to check quick conversions before doing longer calculations.