Octal To Decimal & Decimal To Octal Number Conversion Online Tool

How to use:

• Decimal to Octal:
  • Enter any decimal number you want to convert.
  • Click the “Convert to octal” button, and instantly, you’ll receive the octal representation.
• Octal to Decimal:
  • Enter the binary number you wish to convert.
  • Hit “Convert to decimal,” and just as quickly, you’ll get the decimal equivalent.

What are octal and decimal number systems?

Octal System (Base 8):

It employs eight digits, 0 through 7, to express numerical values. In an octal number, each digit represents a power of 8. The least significant digit denoting 8^0 (1), the subsequent digit representing 8^1 (8), and the following 8^2 (64), and so on. Octal numbers are frequently used in computer programming and telecommunications, facilitating the compact representation of groups of three binary digits (bits) by a single octal digit.

Decimal System (Base 10):

The decimal or base 10 number system consists of 10 single digits from 0 to 9. It is the most commonly used number system in our daily lives, like counting, money, and measurements. It's based on powers of 10, and each position represents a different multiple of 10.

Convert from Octal to Decimal Number System:

Conversion Process :

Below are the steps to convert an octal number to decimal:

Steps:

1. Write down the octal number and identify the place values of each digit. The rightmost digit has a place value of 8⁰ , the next one is 8¹ , and so on.
2. Multiply each digit of the octal number by its corresponding power of 8. Start with the rightmost digit (least significant digit).
3. Example: For octal number 725, the calculation will be:
   • 7×8²=7×64=448
   • 2×8¹=2×8=16
   • 5×8⁰=5×1=5
4. Add all the results together to get the decimal equivalent.
   • 448+16+5=469
5. So, the decimal equivalent of octal 725 is 469 in decimal number system.

Convert from Decimal to Octal Number System:

Conversion Process:

To convert a decimal number to octal, you use division by 8. Below are the steps.

Steps:

1. Divide the decimal number by 8, noting both the quotient and the remainder.
2. Continue dividing the quotient by 8 until the quotient becomes 0, keeping track of all remainders.
3. Write down the remainders in reverse order. This gives you the octal equivalent.
4. Example: Convert 469)₁₀ to octal:
   • 469/8 = 58 remainder 5
   • 58/8 = 7 remainder 2
   • 7/8 = 0 remainder 7
5. So, 469 in decimal is 725 in octal.