Decimal to Octal Converter

What is Decimal to Octal Conversion?

Decimal to octal conversion is the process of transforming a number from the decimal system (base-10) to the octal system (base-8). This conversion is important in computer science and digital systems, particularly in certain programming and hardware contexts where octal representation is useful.

Formula and Representation

The formula for converting a decimal number to octal is:

\[D_{10} = \sum_{i=0}^{n} o_i \cdot 8^i\]

Where:

• \(D_{10}\) is the decimal number
• \(o_i\) represents the octal digits (0 to 7)
• \(i\) is the position of the octal digit (starting from 0)
• \(n\) is the number of octal digits minus 1

Calculation Steps

To convert a decimal number to octal:

1. Divide the decimal number by 8
2. Keep track of the remainder (0 to 7)
3. Continue dividing the quotient by 8 until the quotient becomes 0
4. Read the remainders from bottom to top to get the octal number

Example

Let's convert the decimal number 78 to octal:

\[ \begin{align*} 78 \div 8 &= 9 \text{ remainder } 6 \\ 9 \div 8 &= 1 \text{ remainder } 1 \\ 1 \div 8 &= 0 \text{ remainder } 1 \end{align*} \]

Reading the remainders from bottom to top, we get: 116

Therefore, \(78_{10} = 116_8\)

Visual Representation

This visual representation illustrates the conversion of the decimal number 78 to its octal equivalent 116. The arrow indicates the transformation from base-10 to base-8, demonstrating how a decimal number can be represented using digits from 0 to 7 in the octal system.