Hexadecimal to Binary Converter

How to Convert Hexadecimal to Binary

Converting hexadecimal 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 for converting a hexadecimal number to binary involves replacing each hexadecimal digit with its 4-bit binary equivalent. The formula can be expressed as:

\[ \text{Binary} = \sum_{i=0}^{n-1} (b_i \times 2^i) \]

Where:

• \(b_i\) represents each binary digit (0 or 1)
• \(i\) is the position of the binary digit (starting from 0 for the rightmost digit)
• \(n\) is the total number of binary digits

Conversion Steps

1. Identify each hexadecimal digit in the number.
2. Convert each hexadecimal digit to its 4-bit binary equivalent using a conversion table.
3. Combine all the 4-bit binary equivalents in the same order as the original hexadecimal digits.
4. Remove leading zeros if present (unless the entire result is zero).

Example Conversion

Let's convert the hexadecimal number 2A7 to binary.

Step 1: Identify Hexadecimal Digits

The hexadecimal number 2A7 consists of three digits: 2, A, and 7.

Step 2: Convert Each Digit to Binary

Hex Digit	Binary Equivalent
2	0010
A	1010
7	0111

Step 3: Combine Binary Equivalents

Combining all binary equivalents: 001010100111

Final Result

Therefore, 2A7 in hexadecimal = 001010100111 in binary

Visual Representation

This diagram illustrates the process of converting the hexadecimal number 2A7 to its binary equivalent 001010100111.