Online Decimal to Octal Converter

What are Decimal Numbers?

Decimal numbers are part of the base-10 numbering system, which is the most commonly used system for representing numbers in everyday life. This system employs ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each digit in a decimal number has a place value that is a power of 10.

The decimal system is also known as the Hindu-Arabic numeral system and is integral to various fields such as mathematics, engineering, and science.

What are Octal Numbers?

Octal numbers are part of the base-8 numbering system, which uses eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. This system is less common than the decimal system but is used in computing and digital electronics.

Each digit in an octal number has a place value that is a power of 8. Octal numbers are often used in computer science because they can be easily converted to and from binary numbers, which are used internally by computers.

What is a Decimal to Octal Converter?

A decimal-to-octal converter is a tool that converts decimal (base 10) numbers into octal (base 8) numbers. It is a useful tool for computer scientists and engineers, as it allows them to easily convert decimal numbers into the octal number system, which is often used to represent binary data.

How to Use the Decimal to Octal Conversion Tool?

Using the Decimal to Octal Conversion Tool on LambdaTest is straightforward. Follow these steps to convert your decimal numbers to octal:

Step-by-Step Guide

• Access the Tool: Open your web browser and go to Decimal to Octal Conversion Tool.
• Enter the Decimal Number: Locate the input field under “Decimal” and type or paste the decimal number you want to convert into Octal.
• Convert the Number: After entering the decimal number, click “Convert to Octal”.
• View the Result: The octal equivalent of the entered decimal number will be displayed in the “Output” section. You can copy the octal number for use in your calculations or records.

Example

Let's go through an example:

• Click on “Add Sample File”.
• The decimal number will be displayed in the output, “45 56.6 70 30”.
• Click on “Convert to Octal”.
• The tool will display the octal equivalent, 55 70.46314631 106 36.

Tips for Using the Tool

• Ensure Correct Input: Make sure the number entered is a valid decimal number. The tool will not accept letters or special characters.
• File Upload: You can upload a TXT(Text) file and separate decimal numbers with space to convert many numbers simultaneously, but make sure there are no alphabets or special characters.
• Mobile-Friendly: You can use this tool on your mobile device, making conversions on the go convenient.

How to Convert from Decimal to Octal with Steps?

Converting a decimal number to its octal equivalent involves a process of repeated division by 8, keeping track of the remainder. Here’s a step-by-step guide:

Method 1: Convert Decimal to Octal with Steps:

• Divide the decimal number by 8.
• Record the remainder.
• Update the quotient (the result of the division).
• Repeat the process with the new quotient until the quotient becomes zero.
• Read the remainder in reverse order to get the octal number.

Example 1

Let's convert the decimal number 156 to octal:

• Divide the decimal number (156) by 8:
• 156 ÷ 8 = 19 with a remainder of 4.
• Record the remainder: 4.
• Divide the quotient (19) by 8:
• 19 ÷ 8 = 2 with a remainder of 3.
• Record the remainder: 3.
• Divide the new quotient (2) by 8:
• 2 ÷ 8 = 0 with a remainder of 2.
• Record the remainder: 2.
• Reading the remainders in reverse order (from the last division to the first):
• The remainder are 2, 3, and 4.
• Therefore, the octal representation of 156 is 234.

Example 2

Convert the decimal number 83 to octal:

• Divide 83 by 8:
• 83 ÷ 8 = 10 with a remainder of 3.
• Record the remainder: 3.
• Divide the quotient (10) by 8:
• 10 ÷ 8 = 1 with a remainder of 2.
• Record the remainder: 2.
• Divide the new quotient (1) by 8:
• 1 ÷ 8 = 0 with a remainder of 1.
• Record the remainder: 1.
• Reading the remainder in reverse order:
  • The remainder are 1, 2, and 3.
  • Therefore, the octal representation of 83 is 123.

Example 3

Try converting the decimal number 45 to octal using the steps provided:

• Divide 45 by 8:
• 45 ÷ 8 = 5 with a remainder of 5.
• Record the remainder: 5.
• Divide the quotient (5) by 8:
• 5 ÷ 8 = 0 with a remainder of 5.
• Record the remainder: 5.
• Reading the remainder in reverse order:
• The remainder are 5 and 5.
• Therefore, the octal representation of 45 is 55.

Following these steps, you can accurately convert any decimal number to its octal equivalent.

Method 2: Convert Decimal to Binary to Octal

This method involves converting a decimal number to binary first and then converting the binary number to octal.

Steps to Convert Decimal to Binary:

• Divide the decimal number by 2.
• Record the remainder.
• Update the quotient.
• Repeat the process until the quotient becomes zero.
• Read the remainder in reverse order to get the binary number.

Convert Binary to Octal:

• Group the binary digits into sets of three, starting from the right. Add leading zeros if necessary.
• Convert each group of three binary digits to a single octal digit.

Example 1

Convert decimal 156 to octal:

• Convert 156 to binary:
• 156 ÷ 2 = 78, remainder = 0
• 78 ÷ 2 = 39, remainder = 0
• 39 ÷ 2 = 19, remainder = 1
• 19 ÷ 2 = 9, remainder = 1
• 9 ÷ 2 = 4, remainder = 1
• 4 ÷ 2 = 2, remainder = 0
• 2 ÷ 2 = 1, remainder = 0
• 1 ÷ 2 = 0, remainder = 1
• Binary representation: 10011100.
• Group the binary digits into sets of three (from right to left): 10011100.
• Add leading zeros if necessary: 001 001 110
• Convert each group of three binary digits to octal:
• 001 = 1
• 001 = 1
• 110 = 6
• So, the octal representation is 116.

Decimal to Octal Table

Here is a quick reference table for converting decimal numbers to octal: