Thus, an Octal to Binary Converter is a tool that is used to convert a number represented in octal (base-8) notation to its binary (base-2) equivalent. The tool takes an octal number as input and performs the conversion using a simple process that involves replacing each octal digit with its binary equivalent. This process results in a binary number that is equivalent to the original octal number.
Octal numbers are often used in computer programming to represent sets of three bits at a time, while binary numbers are used to represent individual bits. So, it’s useful to be able to convert between these two numbering systems when working with computer programming. An octal to binary converter can help you quickly and easily convert octal numbers to their binary equivalent, saving you time and effort in your programming work.
Steps to convert Octal to Binary
Converting an octal number to a binary number involves a simple step-by-step process. Here are the steps:
- Write down the octal number.
- Convert each octal digit to a 3-bit binary number. You can do this by replacing each octal digit with its binary equivalent using the table below:
Table 1: Octal to Binary Conversion table
| Octal Digit | Binary Equivalent |
|
0 |
000 |
|
1 |
001 |
|
2 |
010 |
|
3 |
011 |
|
4 |
100 |
|
5 |
101 |
|
6 |
110 |
|
7 |
111 |
- Write the binary equivalents of each octal digit next to each other in order from left to right to form the binary equivalent of the octal number.
Let’s go through an example to illustrate these steps. We will convert the octal number 752 to binary.
- Write down the octal number: 752.
- Convert each octal digit to a 3-bit binary number using the table 1. The octal digit 7 has a binary equivalent of 111. The octal digit 5 has a binary equivalent of 101. The octal digit 2 has a binary equivalent of 010.
- Write the binary equivalents of each octal digit next to each other in order from left to right to form the binary equivalent of the octal number. So, the binary equivalent of the octal number 752 is 111101010.
Solved Examples to convert Octal to Binary
Here are some examples of converting octal numbers to binary:
Example 1: Convert the octal number 73 to binary.
- The given octal number is 73.
- The octal digit 7 has a binary equivalent of 111.
- The octal digit 3 has a binary equivalent of 011.
- So, the binary equivalent of the octal number 73 is 111011.
Example 2: Convert the octal number 456 to binary.
- The given octal number is 456.
- The octal digit 4 has a binary equivalent of 100.
- The octal digit 5 has a binary equivalent of 101.
- The octal digit 6 has a binary equivalent of 110.
- So, the binary equivalent of the octal number 456 is 100101110.
Example 3: Convert the octal number 17 to binary.
- The given octal number is 17.
- The octal digit 1 has a binary equivalent of 001.
- The octal digit 7 has a binary equivalent of 111.
- So, the binary equivalent of the octal number 17 is 001111.