Hexadecimal to Binary Converter

What is Hexadecimal to Binary Conversion?

Hexadecimal to binary conversion is the process of transforming a number from base 16 (hexadecimal) to base 2 (binary). This conversion is frequently used in computer science and digital systems, as it provides a compact representation of binary data.

Conversion Method

The conversion from hexadecimal to binary is straightforward because each hexadecimal digit corresponds to exactly four binary digits (bits). This relationship makes the conversion process simple and direct.

Hexadecimal to Binary Mapping

Here's the mapping of hexadecimal digits to their 4-bit binary equivalents:

Hex | Binary    Hex | Binary
----+---------  ----+---------
 0  | 0000       8  | 1000
 1  | 0001       9  | 1001
 2  | 0010       A  | 1010
 3  | 0011       B  | 1011
 4  | 0100       C  | 1100
 5  | 0101       D  | 1101
 6  | 0110       E  | 1110
 7  | 0111       F  | 1111

Conversion Steps

1. Split the hexadecimal number into individual digits.
2. Convert each hexadecimal digit to its 4-bit binary equivalent using the mapping above.
3. Concatenate the resulting binary groups in the same order as the original hexadecimal digits.

Example

Let's convert the hexadecimal number A3F to binary:

 A    3    F
 |    |    |
1010 0011 1111

Therefore, A3F₁₆ = 101000111111₂

Advantages of Hex to Binary Conversion

• Compact Representation: Hexadecimal provides a more compact way to represent binary data.
• Error Reduction: It's easier for humans to read and transcribe hexadecimal than long strings of binary.
• Simplifies Binary Manipulation: Working with 4-bit groups (hexadecimal) is often more convenient than individual bits.

Understanding the relationship between hexadecimal and binary is crucial in many areas of computer science, including digital logic design, computer architecture, and low-level programming.