Octal to Decimal Converter

Table of Contents

• How does octal to decimal conversion work?
• Octal to decimal conversion formula
• Conversion process
• Example #1
• Example #2
• Octal to decimal conversion table

How does octal to decimal conversion work?

The conversion from octal to decimal is based on interpreting each digit in the octal system (base 8) as a power of 8, starting from the least significant digit (the rightmost). The octal system only uses the digits 0 to 7. To convert an octal number to decimal, multiply each digit by 8 raised to the power corresponding to its position, then sum the results.

Octal to decimal conversion formula

The general formula for converting an octal number to decimal is:

where:

• di is the value of each digit at position i in the octal number (counting from the right, starting at 0).
• i is the position of the digit in the number.

Conversion process

1. Write down the octal number and assign each digit to its corresponding position.
2. Multiply each digit by 8 raised to the power of its position.
3. Sum the results of each calculation to get the final decimal value.

Example #1

Convert the octal number 745 to decimal.

1. Assign positions: 7 in position 2, 4 in position 1, and 5 in position 0.
2. Multiply each digit by 8 raised to its position:
   • 7 × 82 = 7 × 64 = 448
   • 4 × 81 = 4 × 8 = 32
   • 5 × 80 = 5 × 1 = 5
3. Sum the results: 448 + 32 + 5 = 485

Result: The octal number 745 is 485 in decimal.

Example #2

Convert the octal number 123 to decimal.

1. Assign positions: 1 in position 2, 2 in position 1, and 3 in position 0.
2. Multiply each digit by 8 raised to its position:
   • 1 × 82 = 1 × 64 = 64
   • 2 × 81 = 2 × 8 = 16
   • 3 × 80 = 3 × 1 = 3
3. Sum the results: 64 + 16 + 3 = 83

Result: The octal number 123 is 83 in decimal.

Octal to decimal conversion table