Binary to Gray Code Converter

The Binary to Gray Code Converter is a versatile tool designed to convert between binary and Gray code representations. This converter is essential for various applications in digital systems, error correction, and signal processing.

What is Gray Code?

Gray code, also known as reflected binary code, is a sequence of binary numbers where adjacent numbers differ by only one bit. This property makes Gray code useful in reducing errors in digital communications and simplifying certain hardware implementations.

Conversion Formulas

The conversion between binary and Gray code can be expressed as follows:

Binary to Gray Code:

\[ G_i = B_i \oplus B_{i+1} \]

Gray Code to Binary:

\[ B_i = G_i \oplus B_{i+1} \]

Where:

• \(G_i\) is the i-th bit of the Gray code
• \(B_i\) is the i-th bit of the binary code
• \(\oplus\) represents the XOR operation

Conversion Steps

Binary to Gray Code:

1. The most significant bit (leftmost) of the Gray code is the same as the binary.
2. Each subsequent bit is the XOR of the current binary bit and the previous binary bit.

Gray Code to Binary:

1. The most significant bit of the binary is the same as the Gray code.
2. Each subsequent bit is the XOR of the current Gray code bit and the previous binary result.

Example with Visual Representation

Let's visualize the conversion of binary 1010 to Gray code:

This visual representation illustrates the binary to Gray code conversion process. The final result shows that the binary number 1010 is equivalent to the Gray code 1111. This method provides a clear and intuitive understanding of the conversion process, which is crucial in digital systems and error correction techniques.