Base 8 Calculator

Formula

To calculate the Decimal Value (V) from a Base 8 number:

\[ V = \sum (D_n \times 8^n) \]

Where:

\(V\) is the value in decimal
\(D_n\) is the nth digit in the octal number
\(n\) is the position of the digit from the right, starting from 0

What is Base 8?

Base 8, also known as octal, is a number system that uses eight digits, from 0 to 7. It is a positional numeral system, meaning the value of a digit depends on its position. It is commonly used in computing systems, particularly for representing file permissions in Unix-like operating systems.

Example Calculation 1

Let's assume the following value:

Base 8 Number = 123

Using the formula:

\[ V = 1 \times 8^2 + 2 \times 8^1 + 3 \times 8^0 = 1 \times 64 + 2 \times 8 + 3 \times 1 = 64 + 16 + 3 = 83 \]

The Decimal Value is 83.

Example Calculation 2

Let's assume the following value:

Base 8 Number = 456

Using the formula:

\[ V = 4 \times 8^2 + 5 \times 8^1 + 6 \times 8^0 = 4 \times 64 + 5 \times 8 + 6 \times 1 = 256 + 40 + 6 = 302 \]

The Decimal Value is 302.