Decimal to Octal: Meaning, Conversion Steps

To change a decimal to octal, you keep dividing it by 8 and keeping track of the remainders. When you read these remainders from bottom to top, they make the octal equivalent. It is an important ability in computing to know how to use shorthand for binary.

It can feel like learning a hidden code to understand how numbers change between different systems. The decimal system (Base-10) uses ten digits (0–9) in your daily life. But the octal system (Base-8) is frequently better for computers and digital systems. You are looking at the process of converting a decimal to octal if you have ever wondered how a normal number like 100 changes into something completely different in a computer's "brain." This method makes it easier to switch from our normal counting system to the world of eight digits, so you can solve these issues quickly and correctly.

What is the Decimal to Octal Conversion?

Before we go into the procedures, we need to know what these systems really mean. We usually count in tens. There are ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

The octal system, on the other hand, is based on 8. This means it only has eight digits: 0, 1, 2, 3, 4, 5, 6, and 7. You won't ever see a "8" or "9" in an octal number that is formatted correctly. The conversion of decimal to octal is the same process as changing a base-10 number into a base-8 number. Octal is a great way to shorten long binary strings, which is very helpful in computer programming and digital electronics.

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How to Convert Decimal to Octal?

The Double Dabble or "Successive Division" approach is the best way to decimal to octal conversion. The number 8 is our main instrument for division now that we are shifting to a base-8 system.

Step-by-Step Conversion Process

• Break the number down: If you have a decimal number, divide it by 8.

• Pay attention to the rest: Put the rest on the side. This number will always be between 0 and 7.

• Change the quotient: Get the complete number result from the last step. Once more, divide this new number by 8.

• Stop at zero: Keep doing this until your quotient is zero.

• Look at the result: To find the octal value, read the remainders from the bottom to the top. The final remainder found is the most important digit.

Decimal to Octal Conversion Examples

It's lot easier to learn when you can see the process in action. Let's look at a few examples of decimal to octal conversion examples with different numbers.

Example 1: Convert 150 to Octal

• 150 / 8 = 18 with a remainder of 6

• 18 / 8 = 2 with a remainder of 2

• 2 / 8 = 0 with a remainder of 2

Reading from bottom to top, the octal equivalent of 150 is 226.

Example 2: Convert 450 to Octal

• 450 / 8 = 56 with a remainder of 2

• 56 / 8 = 7 with a remainder of 0

• 7 / 8 = 0 with a remainder of 7

Reading from bottom to top, the decimal number 450 is written as 702 in octal.

Decimal to Octal Converter with Solution Table

If you like to have things laid out visually, a table is the easiest way to decimal to octal converter with solution. Let's change the number 95 from decimal to binary.

Result: Reading upwards, 95 in decimal is 137 in octal.

Converting Decimal to Octal with Solutions

Sometimes, you might encounter a number with a fractional part (like 0.125). To perform decimal to octal with solution for fractions, we use multiplication instead of division.

1. Multiply the fraction by 8.

2. Note the integer part: The whole number before the decimal point becomes your first octal digit.

3. Repeat with the remaining fraction: Take the new fractional part and multiply by 8 again.

4. Read downwards: Unlike the division method, you read these digits from top to bottom.

Example: Convert 0.125 to Octal

• 0.125 x 8 = 1.000 (Integer part is 1, remainder is 0)

• The process stops because the fraction is zero.

• Result: 0.125 in decimal is 0.1 in octal.

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How to Convert Octal to Decimal? 

While we have focused on moving from our standard system into base-8, it is equally important to know how to go back. If you have an octal value and want to understand its actual quantity in our everyday terms, you need to convert octal to decimal.

Steps to Convert Octal to Decimal

To reverse the process, we use the "Positional Notation" method. Instead of dividing, we multiply each digit by powers of 8.

• Identify the positions: Assign a power of 8 to each digit, starting from the rightmost digit (which is 8^0) and moving left (8^1, 8^2, etc.).

• Multiply: Multiply each digit of the octal number by its corresponding power of 8.

• Sum it up: Add all the products together to get the final decimal value.

Octal to Decimal Example

Let’s convert the octal number 137 back into a decimal number to see how the math works.

• Digit 7 (Position 0): 7 \times 8^0 = 7 \times 1 = 7

• Digit 3 (Position 1): 3 \times 8^1 = 3 \times 8 = 24

• Digit 1 (Position 2): 1 \times 8^2 = 1 \times 64 = 64

Sum: 64 + 24 + 7 = 95.

So, the octal number 137 is equal to the decimal number 95.

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Practice Questions on Decimal to Octal Conversion

Testing your skills is the best way to ensure you have mastered the decimal to octal logic. 

Convert the Following Decimal Numbers to Octal

• 64

• 125

• 512

Convert the Following Octal Numbers to Decimal

• 75

• 100

Answer Key

Use this key to check your progress. If you missed any, try the division or multiplication steps again!

• 1. Answer: 100 (64 / 8 = 8 R 0; 8 / 8 = 1 R 0; 1 / 8 = 0 R 1)

• 2. Answer: 175 (125 / 8 = 15 R 5; 15 / 8 = 1 R 7; 1 / 8 = 0 R 1)

• 3. Answer: 1000 (512 / 8 = 64 R 0; 64 / 8 = 8 R 0; 8 / 8 = 1 R 0; 1 / 8 = 0 R 1)

• 4. Answer: 61 ((7 \times 8) + (5 \times 1))

• 5. Answer: 64 ((1 \times 64) + (0 \times 8) + (0 \times 1))

Why Do We Use Octal?

You might be wondering why we bother to convert octal to decimal or the other way around. In the past, octal was popular because it organised bits (binary digits) into sets of three. Since 2^3 = 8, one octal digit can stand for exactly three binary digits. Engineers could read and fix code much more easily now that it wasn't just a long, confused string of 1s and 0s.

Quick Tips for Mental Maths to convert Decimal to Octal

• Check the numbers: You made a mistake if your answer has an 8 or a 9. There are just seven octal digits.

• Powers of 8: If you can remember the first several powers of 8 (8, 64, 512), it will be easier to tell if your answer is close.

• Small Numbers: In octal, any decimal number from 0 to 7 is the same!

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