Octal to Decimal Converter

The Octal to Decimal Converter is an essential tool for converting numbers from the octal (base-8) system to the decimal (base-10) system. This calculator is particularly useful in computer science, digital electronics, and number system conversions.

What is Octal to Decimal Conversion?

Octal to decimal conversion is the process of transforming a number represented in the octal numeral system (using digits 0-7) to its equivalent in the decimal numeral system (using digits 0-9). This conversion is fundamental in understanding and working with different number systems used in computing and digital systems.

Conversion Formula

To convert an octal number to its decimal equivalent, we use the following formula:

\[ \text{Decimal} = \sum_{i=0}^{n-1} d_i \cdot 8^i \]

Where:

• \(d_i\) represents each digit in the octal number
• \(i\) is the position of the digit from right to left, starting at 0
• \(n\) is the total number of digits in the octal number
• The sum gives us the equivalent decimal value

Calculation Steps

Let's convert the octal number 347 to its decimal equivalent:

1. \(7 \cdot 8^0 = 7 \cdot 1 = 7\)
2. \(4 \cdot 8^1 = 4 \cdot 8 = 32\)
3. \(3 \cdot 8^2 = 3 \cdot 64 = 192\)

Sum the results: \(7 + 32 + 192 = 231\)

Therefore, the octal number 347 is equivalent to the decimal number 231.

Example with Visual Representation

Let's visualize the conversion of 347 (octal) to its decimal equivalent:

This visual representation illustrates how each digit in the octal number corresponds to a power of 8. The sum of the products of each digit and its corresponding power of 8 gives us the equivalent decimal value.