Octal to Binary Converter Online

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. Each digit in an octal number has a place value that is a power of 8. This system is used in computing and digital electronics because it can easily be converted to and from binary, which is base-2.

What are Binary Numbers?

Binary numbers are part of the base-2 numbering system, which uses only two digits: 0 and 1. Each digit in a binary number represents an increasing power of 2, starting from the rightmost digit. Binary is the fundamental language of computers, as it is used for all internal operations.

What is Octal to Binary Conversion?

Octal to Binary conversion involves translating a number from the base-8 system to the base-2 system. This is important in computing and digital electronics because binary numbers are the most fundamental data representation within computers, while octal numbers provide a more human-readable form.

How to Use the Octal to Binary Conversion Tool?

Using the Octal to Binary Conversion Tool on LambdaTest is easy. Follow these steps to convert your octal numbers to binary:

• Access the Tool: Open your web browser and go to Octal to Binary Conversion Tool.
• Enter the Octal Number: Locate the input field below “Octal” and type, paste, upload or import the octal number you wish to convert.
• Convert the Number: After entering the octal number, click on the “Convert to Binary” button.
• View the Result: The binary equivalent of the entered octal number will be instantly displayed in “Output”.

Tips for Using the Tool

• Check Input: Ensure the number entered is a valid octal number (digits 0-7).
• File Upload/Load via URL: You can upload a .txt file or import from a URL to import an octal number.
• Mobile-Friendly: The tool works seamlessly on mobile devices, making it convenient to use on the go.
• Convert Multiple Octal Numbers: Separate each octal number with space to convert multiple octal numbers to binary.

How to Convert Octal to Binary?

Method 1: Direct Method of Octal to Binary Conversion

The direct method of converting octal numbers to binary involves converting each octal digit directly to its equivalent three-digit binary representation. This method is straightforward and does not require intermediate conversion to decimal.

Step-by-Step Guide

• Write down the octal number.
• Convert each octal digit to its three-digit binary number.
• Combine the binary groups to form the final binary number.

Solved Example

Convert octal 145 to binary:

• Write down the octal number: 145
• Convert each digit using the table:
• 1 in octal = 001 in binary
• 4 in octal = 100 in binary
• 5 in octal = 101 in binary
• Combine the binary groups: 145 in octal = 001100101 in binary

So, 145 in octal is 001100101 in binary

Another Example

Convert octal 73 to binary:

• Write down the octal number: 73
• Convert each digit using the table:
• 7 in octal = 111 in binary
• 3 in octal = 011 in binary
• Combine the binary groups: 73 in octal = 111011 in binary

So, 73 in octal is 111011 in binary

Practice Problem

Convert octal 27 to binary using the direct method:

• Write down the octal number: 27
• Convert each digit using the table:
• 2 in octal = 010 in binary
• 7 in octal = 111 in binary
• Combine the binary groups: 27 in octal = 010111 in binary

So, 27 in octal is 010111 in binary.

Method 2: Octal to Decimal and then Decimal to Binary

This method involves two main steps: first, converting the octal number to a decimal number, and then converting the resulting decimal number to a binary number. Here’s how to do it step by step:

Step 1: Convert Octal to Decimal

• Identify each digit in the octal number.
• Multiply each digit by 8 raised to the power of its position from right to left, starting at 0.
• Sum the results of these multiplications.

Example 1:

Convert octal 145 to decimal:

• Identify the digits: 1, 4, and 5.
• 1×8² = 1×64=64
• 4× 8¹ = 4×8=32
• 5×8⁰ = 5×1=5
• Sum the results: 64+32+5=101

So, 145 in octal is 101 in decimal.

Step 2: Convert Decimal to Binary

To convert a decimal number to binary, follow these steps:

• Divide the decimal number by 2.
• Record the remainder (this will be a binary digit).
• Update the quotient (the result of the division).
• Repeat the process with the new quotient until the quotient is zero.
• Read the remainder in reverse order to get the binary number.

Example:

Convert decimal 101 to binary:

• Divide by 2: 101÷2 = 50, remainder 1.
• Divide by 2: 50÷2 = 25, remainder 0.
• Divide by 2: 25÷2 = 12, remainder 1.
• Divide by 2: 12÷2 = 6, remainder 0.
• Divide by 2: 6÷2 = 3, remainder 0.
• Divide by 2: 3÷2 = 1, remainder 1.
• Divide by 2: 1÷2 = 0, remainder 1.

Reading the remainders in reverse order, 101 in decimal is 1100101 in binary.

Combining Both Steps:

• Convert 145 octal to decimal: 145 octal = 101 decimal.
• Convert 101 decimal to binary: 101 decimal = 1100101 binary.

Therefore, 145 in octal is 1100101 in binary.

Practice Problem:

Convert octal 27 to binary using the steps provided:

• Convert 27 octal to decimal:
• 2 × 8¹ = 2 × 8 = 16
• 7 × 8⁰ = 7 × 1 = 7
• Sum: 16 + 7 = 23
• Convert 23 decimal to binary:
• 23 ÷ 2 = 11, remainder 1
• 11 ÷ 2 = 5, remainder 1
• 5 ÷ 2 = 2, remainder 1
• 2 ÷ 2 = 1, remainder 0
• 1 ÷ 2 = 0, remainder 1
• Reading the remainders in reverse order, 23 in decimal is 10111 in binary.

So, 27 in octal is 10111 in binary.

Convert Octal to Binary Using Table

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