Hex to Binary Converter

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In computer science and electronics, the hexadecimal (base-16) numeral system is widely used for its more compact representation of numbers compared to binary (base-2). Hexadecimal uses 16 distinct symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen. Converting hexadecimal numbers to binary is an essential skill for those working with digital systems and programming.

In this article, we will explore the process of converting hexadecimal numbers to binary, including the step-by-step method and using programming languages for automation.

1. Step-by-Step Conversion Method

To manually convert a hexadecimal number to binary, you can follow these steps:

  1. Break the hexadecimal number into individual digits.
  2. Convert each hexadecimal digit to its equivalent 4-bit binary representation.
  3. Concatenate the binary representations to obtain the final result.

Example: Convert the hexadecimal number 3A9 to binary. 

Step 1: Break the hexadecimal number into digits: 3, A, 9
Step 2: Convert each digit to binary: 3 = 0011, A = 1010, 9 = 1001
Step 3: Concatenate the binary representations: 0011 1010 1001

The binary equivalent of the hexadecimal number 3A9 is 001110101001.

2. Hexadecimal to Binary Reference Table

To simplify the conversion process, you can use a reference table that maps each hexadecimal digit to its equivalent 4-bit binary representation.

Hexadecimal Binary
0 0000
1 0001

3. Using Programming Languages for Conversion

In addition to manual conversion methods, you can use programming languages to automate the process of converting hexadecimal numbers to binary. Most programming languages, such as Python, C++, and Java, provide built-in functions or libraries to perform this conversion easily. Here's an example using Python: 

hexadecimal_number = '3A9'
binary_number = bin(int(hexadecimal_number, 16))[2:]
print(binary_number)

This short code snippet converts the hexadecimal number 3A9 to binary and prints the result, which is 001110101001.