Octal to Binary converter is an online tool to convert octal data to binary data. Try the below converter now!
Octal (base-8) and binary (base-2) are two common number systems used in the fields. The octal system is often used as a shorthand for binary because each octal digit represents exactly three binary digits (bits). Converting octal to binary is a fundamental skill in digital systems, especially when working with memory addresses, machine code, and data representation.
What is Octal?
The octal number system is a base-8 numeral system that uses eight symbols: 0 through 7. It is often used in computer systems because it provides a more compact way to represent binary numbers. Each octal digit represents three binary digits, making octal a shorthand for binary sequences.
- Example: 725 (octal)
Each octal digit corresponds to a group of three binary digits:
7258 = 7×82+2×81+5×80 = 46910What is Binary?
The binary number system is a base-2 system that uses only two digits: 0 and 1. It is the foundation of all modern computers and digital systems, where 1 represents “on” and 0 represents “off.”
- Example: 101011 (binary)
Each binary digit (bit) represents a power of 2, starting from the right.
Octal to Binary Conversion
Converting octal numbers to binary is straightforward because each octal digit corresponds to exactly three binary digits. This is because 8 is (2^3), meaning each octal digit can be represented by a 3-bit binary number.
- Octal digit: 0, 1, 2, 3, 4, 5, 6, 7
- Binary equivalent: 000, 001, 010, 011, 100, 101, 110, 111
Steps to Convert Octal to Binary
- Convert each octal digit to its 3-bit binary equivalent using the octal-to-binary conversion table.
- Concatenate the binary values to get the full binary number.
Example Conversions
Let’s look at a few examples of converting octal numbers to binary.
Example 1: Convert 725 (octal) to binary.
- Convert each octal digit to binary:
- 7 (octal) = 111 (binary)
- 2 (octal) = 010 (binary)
- 5 (octal) = 101 (binary)
- Concatenate the binary digits: 111010101
So, 725 (octal) is equal to 111010101 (binary).
Example 2: Convert 345 (octal) to binary.
- Convert each octal digit to binary:
- 3 (octal) = 011 (binary)
- 4 (octal) = 100 (binary)
- 5 (octal) = 101 (binary)
- Concatenate the binary digits: 011100101
So, 345 (octal) is equal to 011100101 (binary).
Example 3: Convert 12 (octal) to binary.
- Convert each octal digit to binary:
- 1 (octal) = 001 (binary)
- 2 (octal) = 010 (binary)
- Concatenate the binary digits: 001010
So, 12 (octal) is equal to 001010 (binary).
Octal to Binary Conversion Table
Here’s a quick reference table showing the conversion of octal digits to their binary equivalents:
| Octal | Binary |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
Online Octal to Binary Converter
Online tools provide a fast and efficient way to convert octal numbers to binary, especially when working with long sequences of digits. These tools are commonly used in fields like computer science, digital electronics, and networking.
Steps to Use an Online Converter
- Enter the octal number in the input field.
- Click the “Convert” button.
- The tool will display the equivalent binary number.