Octal to Decimal Converter

Convert Octal to Decimal

Enter an octal number below to convert it to decimal. Our converter handles octal numbers of any length.

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Please enter a valid octal number (0-7 only).

How to Convert Octal to Decimal

Converting octal numbers to decimal is a fundamental operation in computer science and number systems. Here's a comprehensive guide on how to perform this conversion:

Conversion Formula

The process of converting octal to decimal involves multiplying each digit by a power of 8 and summing the results. The general formula is:

\[Decimal = \sum_{i=0}^n d_i \times 8^i\]

Where:

  • \(d_i\) represents each octal digit (0-7)
  • \(i\) is the position of the digit from right to left, starting at 0
  • \(n\) is the number of digits minus 1

Conversion Steps

  1. Identify the place value of each digit (powers of 8).
  2. Multiply each digit by its place value.
  3. Sum up all the resulting products.

Example Conversion

Let's convert the octal number 253 to decimal.

Step 1: Identify place values

2 is in the 8² place

5 is in the 8¹ place

3 is in the 8⁰ place

Step 2: Apply the formula

\(2 \times 8^2 + 5 \times 8^1 + 3 \times 8^0\)

Step 3: Calculate

\(2 \times 64 + 5 \times 8 + 3 \times 1\)

\(128 + 40 + 3\)

Step 4: Sum up

\(171\)

Final Result

Therefore, 253 in octal = 171 in decimal

Visual Representation

253 Octal Conversion Steps: 2 × 8² = 2 × 64 = 128 5 × 8¹ = 5 × 8 = 40 3 × 8⁰ = 3 × 1 = 3 128 + 40 + 3 = 171 Convert 171 Decimal Place Values: 2 in position 2 (8²) 5 in position 1 (8¹) 3 in position 0 (8⁰) Total = 171₁₀

This diagram illustrates the process of converting the octal number 253 to its decimal equivalent 171.

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