Binary to Hexadecimal Converter

The Binary to Hexadecimal Converter is a sophisticated tool designed to transform numbers from the binary system (base-2) to the hexadecimal system (base-16). This calculator is invaluable in computer science, digital electronics, and various mathematical applications.

What is Binary to Hexadecimal Conversion?

Binary to hexadecimal conversion is the process of changing a number represented in the binary numeral system (using only 0s and 1s) to its equivalent in the hexadecimal numeral system (using digits 0-9 and letters A-F). This conversion is crucial in computing as it provides a more compact representation of binary data.

Conversion Formula

The mathematical formula for converting a binary number to hexadecimal involves grouping binary digits and converting each group separately:

\[H = \sum_{i=0}^{n-1} b_i \cdot 16^i\]

Where:

• \(H\) is the hexadecimal equivalent
• \(b_i\) is the value of the \(i\)-th group of 4 binary digits (0-15)
• \(n\) is the number of 4-bit groups
• \(i\) is the position of the group, starting from right to left (0-indexed)

Calculation Steps

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

1. Group the binary digits into sets of four, starting from the right.
2. Convert each group of four binary digits to its hexadecimal equivalent (0-F).
3. Concatenate the hexadecimal digits from left to right.

Example with Visual Representation

Let's convert the binary number 1010 1101 to hexadecimal:

\[ \begin{align*} 1010 \space 1101_2 &= \text{(1010)}_2 \space \text{(1101)}_2 \\ &= \text{A}_\text{16} \space \text{D}_\text{16} \\ &= \text{AD}_\text{16} \end{align*} \]

This visual representation illustrates how the binary number is grouped and converted to its hexadecimal equivalent. The subscript 2 denotes binary, while 16 denotes hexadecimal.