Convert Octal to Binary

Table of Contents  

• What are Octal and Binary Number Systems?
• What is Octal to Binary Conversion?
• How to Convert Octal to Binary
• Octal to Binary Chart
• Octal to Binary Table
• Octal to Binary Example
• Step-by-Step Conversion Method
• Formula for Octal to Binary
• Applications of Octal to Binary in Computers
• Common Misconceptions
• Fun Facts
• Solved Examples
• Conclusion
• FAQs on Convert Octal to Binary

What are Octal and Binary Number Systems?

To understand octal to binary, we first need to know what the octal and binary number systems are.  

Octal Number System (Base 8):  

 It uses 8 digits: 0 to 7.  

 Each digit's place value is a power of 8.  

Binary Number System (Base 2):  

 It uses only 2 digits: 0 and 1.  

 Each digit's place value is a power of 2.  

What is Octal to Binary Conversion?

Octal to binary conversion is the process of changing a number from base 8 to base 2. This is essential in computer systems because computers use binary. Octal is a shorter way to write binary numbers. Each octal digit can be written as 3 binary digits (0s and 1s). This makes conversion quick and easy.

How to Convert Octal to Binary

To convert octal to binary, follow these simple steps:  

• Take each digit of the octal number.  

• Convert each octal digit into a 3-digit binary number.  

• Join all binary groups together to form the final binary number.  

Octal to Binary Chart

Use the octal to binary chart below to simplify the conversion process.  

This chart helps you avoid manual calculations and speeds up conversions.

Octal to Binary Table

Here is an extended octal to binary table to show how multiple digits are converted:  

This table gives a clear visual of actual conversions.

Octal to Binary Example

Here is an example with a step-by-step explanation:  

Example: Convert the octal number 275 to binary.  

 2 in binary = 010  

 7 in binary = 111  

 5 in binary = 101  

Now join: 275 (octal) = 010111101 (binary)  

Here’s another example: Convert 41 (octal) to binary:  

 4 = 100, 1 = 001 → 100001  

Step-by-Step Conversion Method

Let’s learn the full method for converting octal to binary clearly:  

• Write down the octal number.  

• Use the octal to binary chart to find 3-digit binary equivalents.  

• Convert each digit individually.  

• Combine the binary groups.  

• You can remove extra zeros at the start unless you need a fixed number of digits.  

Example: Convert the octal number 157 to binary.

Step 1: Write down the octal number: 157

Step 2: Convert each octal digit using the 3-bit binary chart:

• 1 → 001

• 5 → 101

• 7 → 111

Step 3: Combine the binary groups: 001 101 111

Step 4: Remove unnecessary leading zeros (optional): 1101111

Answer: 157 (octal) = 1101111 (binary)

Formula for Octal to Binary

There is no calculation formula for octal to binary. Just use the chart to match each octal digit with its 3-digit binary number.

Example: Convert the octal number 264 to binary.

Step 1: Break each octal digit: 2, 6, 4

Step 2: Convert each digit using the 3-bit binary chart:

• 2 → 010

• 6 → 110

• 4 → 100

Step 3: Join the binary groups: 010 110 100

Step 4: Remove unnecessary leading zeros (optional): 10110100

Answer: 264 (octal) = 10110100 (binary)

Applications of Octal to Binary in Computers

• Digital Electronics: Octal makes it easier to read long binary numbers.  

• Programming: Permissions in Unix/Linux use octal values.  

• Memory Addresses: Octal helps shorten memory binary codes.  

• Microprocessor Programming: Binary instructions are grouped as octal.  

• Error Checking: Octal simplifies grouping bits during debugging.  

Common Misconceptions

Let’s address some myths about octal to binary conversion:  

• You must divide by 2 to convert.  

Wrong! Octal to binary uses a 3-bit mapping, not division.  

• Binary groups are 2 digits.  

No! Octal to binary requires 3-digit groups.  

• You can mix digits from different conversions.  

Never! Each octal digit has a fixed 3-digit binary match.  

• You don’t need any math. Just match each octal digit to its 3-digit binary number. 

Not needed. Mapping from the chart is enough.  

• Leading zeros in binary matter.  

Leading zeros can be removed unless the context requires a fixed bit length.  

Fun Facts

• Changing octal to binary is faster than decimal to binary because each octal digit becomes 3 binary digits directly.

• Early computers like the PDP-11 used octal for programming.  

• Octal helps show numbers in memory more clearly because it uses fewer digits than binary.

• In Unix/Linux, octal numbers like 755 are used to set who can read, write, or run a file

• You can easily convert large binary values to octal by grouping the binary into 3s from right to left.  

Solved Examples

Let’s solve some practical problems involving octal to binary:  

Example 1:

Q: Convert 36 (octal) to binary.

Step 1: Break the octal digits: 3, 6
Step 2: Convert each digit to 3-bit binary:

• 3 → 011

• 6 → 110
  Step 3: Join the binary groups: 011 110

Answer: 36 (octal) = 011110 (binary)

Example 2:

Q: Convert 720 (octal) to binary.

Step 1: Break the octal digits: 7, 2, 0
Step 2: Convert each digit to 3-bit binary:

• 7 → 111

• 2 → 010

• 0 → 000
  Step 3: Join the binary groups: 111 010 000

Answer: 720 (octal) = 111010000 (binary)

Example 3:

Q: Convert 11 (octal) to binary.

Step 1: Break the octal digits: 1, 1
Step 2: Convert each digit to 3-bit binary:

• 1 → 001

• 1 → 001
  Step 3: Join the binary groups: 001 001

Answer: 11 (octal) = 001001 (binary)

Example 4:

Q: Convert 504 (octal) to binary.

Step 1: Break the octal digits: 5, 0, 4
Step 2: Convert each digit to 3-bit binary:

• 5 → 101

• 0 → 000

• 4 → 100
  Step 3: Join the binary groups: 101 000 100

Answer: 504 (octal) = 101000100 (binary)

Example 5: Convert 1001 (octal) to binary.  

 1 = 001, 0 = 000, 0 = 000, 1 = 001 → Answer: 001000000001  

Conclusion

Mastering octal to binary conversion is an essential step in understanding computer logic and programming systems. It’s easier than you might think—just use the octal to binary chart or table to break down each digit into a 3-bit binary format.  

Grasping how to convert octal to binary will help you with faster data conversion and strengthen your foundation in digital electronics. Practice with more examples and memorise the basic conversion pairs.

Frequently Asked Questions on Converting Octal to Binary

1. How do you convert octal to binary?

Answer: Convert each octal digit to its 3-bit binary equivalent.

2. How do you convert 145 octal to binary?

Answer: Octal 145 becomes binary 001100101, or 1100101 if you remove extra zeros at the start.

3. What is 326 octal in binary?

Answer: Octal 326 becomes binary 011010110, or 11010110 after removing starting zeros.

4. What is the binary equivalent of 225 in octal?

Answer: 225₈ = 010 010 101 → Binary = 10010101

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