Hexadecimal to Binary

Hexadecimal and binary are two widely used number systems in computer science and digital electronics. Understanding how to convert between these systems is essential for anyone working in fields related to computing, data representation, or digital circuitry.

Hexadecimal (Base 16): This system uses 16 symbols: 0-9 to represent values zero to nine and A-F (or a-f) to represent values ten to fifteen.
Binary (Base 2): This system uses only two symbols: 0 and 1.

In this article, we’ll explore how to convert a hexadecimal number to its binary equivalent. We’ll break down the conversion process step by step and provide examples to ensure a clear understanding.

Table of Contents

Why Convert Hexadecimal to Binary?

Hexadecimal numbers are often used in programming and digital systems because they provide a more compact representation of binary data. For example, a single hexadecimal digit represents four binary digits (bits). This makes it easier to read and write long binary sequences.

Hexadecimal to Binary Conversion Process

Converting a hexadecimal number to binary is straightforward. Each hexadecimal digit is directly mapped to a four-bit binary equivalent. Below is the conversion table:

Hexadecimal	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
A (10)	1010
B (11)	1011
C (12)	1100
D (13)	1101
E (14)	1110
F (15)	1111

Step-by-Step Conversion Example

Let’s take the hexadecimal number 2F3 and convert it to binary.

Step 1: Break Down the Hexadecimal Number

Start by writing down the hexadecimal number and break it down into individual digits:

Step 2: Convert Each Hexadecimal Digit to Binary

Using the conversion table, convert each digit to its corresponding binary value:

2 in binary is 0010.
F (which represents 15 in decimal) in binary is 1111.
3 in binary is 0011.

Step 3: Combine the Binary Values

Now, concatenate all the binary values obtained:

2 → 0010
F → 1111
3 → 0011

So, the binary equivalent of hexadecimal 2F3 is 0010 1111 0011.

Another Example

Let’s convert the hexadecimal number A9C to binary.

Step 1: Break Down the Hexadecimal Number

Step 2: Convert Each Hexadecimal Digit to Binary

A (which represents 10 in decimal) in binary is 1010.
9 in binary is 1001.
C (which represents 12 in decimal) in binary is 1100.

Step 3: Combine the Binary Values

A → 1010
9 → 1001
C → 1100

The binary equivalent of hexadecimal A9C is 1010 1001 1100.

Practice Problem

Try converting the hexadecimal number 3B7 to binary using the steps provided above.

Solution:

3 in binary is 0011.
B (which represents 11 in decimal) in binary is 1011.
7 in binary is 0111.

The binary equivalent of 3B7 is 0011 1011 0111.

Conclusion

Converting from hexadecimal to binary is a crucial skill in various fields related to computing and electronics. By following the simple steps outlined in this guide, you can easily convert any hexadecimal number into its binary equivalent. This process, once practiced, becomes second nature and is fundamental for tasks such as programming, debugging, and understanding digital circuit designs.