Octal to Binary Converter

How to Convert Octal to Binary

Converting octal numbers to binary is a fundamental operation in computer science and digital systems. Here's a comprehensive guide on how to perform this conversion:

Conversion Formula

The process of converting octal to binary involves mapping each octal digit to its 3-bit binary equivalent. The general formula is:

\[Octal_{(8)} = (d_n d_{n-1} ... d_1 d_0)_8 = (b_m b_{m-1} ... b_1 b_0)_2 = Binary_{(2)}\]

Where:

• \(d_i\) represents each octal digit (0-7)
• \(b_j\) represents each binary digit (0 or 1)
• \(n\) is the number of octal digits
• \(m = 3n\) is the number of binary digits

Conversion Steps

1. Start from the leftmost digit of the octal number.
2. Convert each octal digit to its 3-bit binary equivalent.
3. Combine all the 3-bit binary groups.
4. Remove any leading zeros from the final binary number.

Example Conversion

Let's convert the octal number 253 to binary.

Step 1: Convert Each Octal Digit

2 = 010

5 = 101

3 = 011

Step 2: Combine Binary Groups

010 101 011

Step 3: Remove Leading Zeros

10101011

Final Result

Therefore, 253 in octal = 10101011 in binary

Visual Representation

This diagram illustrates the process of converting the octal number 253 to its binary equivalent 10101011.