About

In computer science education, understanding positional notation is fundamental. This tool translates Octal (base-8) numbers into standard Decimal (base-10) integers, but it serves a dual purpose: calculation and demonstration. Unlike simple converters, this utility offers a "Show Steps" feature that deconstructs the input number, showing how each digit is multiplied by increasing powers of 8. This is invaluable for students learning binary math or engineers reverse-engineering legacy data formats where octal encoding was common. The logic supports large integer strings, ensuring accuracy where standard calculators might resort to scientific notation.

Formulas

The value of an octal number is the sum of its digits multiplied by their respective position's power of 8.

D = n∑i=0 d_i × 8ⁱ

Example for Octal 25:

(2 × 8¹) + (5 × 8⁰) = 16 + 5 = 21

Reference Data

Power of 8	Expansion	Decimal Value
8⁰	1	1
8¹	8	8
8²	8 × 8	64
8³	8 × 8 × 8	512
8⁴	8 × 8 × 8 × 8	4,096
8⁵	...	32,768
8⁶	...	262,144
8⁷	...	2,097,152
8⁸	...	16,777,216

Frequently Asked Questions

This specific tool is optimized for the Octal to Decimal direction to show the multiplication steps. Please use our Decimal to Octal tool for the reverse process involving division/remainders.

The rightmost digit is position 0 (8^0 = 1). Moving left, the position index increases (8^1, 8^2, etc.). Each digit is multiplied by 8 raised to its position index.

The tool will display an error. In the base-8 system, the only valid digits are 0 through 7. "8" is not a valid symbol in this numbering system.

The interface is designed to handle standard integer sizes up to 32 digits gracefully, though the calculation logic uses BigInt to support even larger values for advanced use cases.