Gray Code to Binary Code in C++

A binary number system in which two successive values differ by just one bit is called grey code, sometimes referred to as reflected binary code. It has uses in a number of industries, such as rotary encoders and digital communications. In digital electronics and computer programming, converting Grey code to binary code is a frequent process. Using the Gray-to-Binary conversion process and iterating through the Grey code bits, you may write a C++ program that converts Grey code to binary code. Every Grey code bit is XORed with the subsequent higher-order bit as part of the process. Moving from the most important to the least important bit in order of significance

Gray to Binary Conversion:

• The binary code's Most Significant Bit (MSB) and the grey code's MSB are always the same.
• The binary code bit at that position and the preceding index can be XORed to generate further bits of the output grey code.

EX: Binary: 0011

 Gray : 0010

 To convert binary 0011 to Gray code:

• The leftmost bit remains the same (0).
• For the second bit, XOR is with the first bit in the binary code (0 XOR 0 = 0).
• For the third bit, XOR is with the second bit in the binary code (0 XOR 1 = 1).
• For the fourth bit, XOR is with the third bit in the binary code (1 XOR 1 = 0).
• So, the Gray code 0010 is indeed correct for the binary code 0011.

 Binary: 01001

 Gray: 01101

 To convert binary 01001 to Gray code:

• The leftmost bit remains the same (0).
• For the second bit, XOR is with the first bit in the binary code (0 XOR 1 = 1).
• For the third bit, XOR is with the second bit in the binary code (1 XOR 0 = 1).
• For the fourth bit, XOR is with the third bit in the binary code (1 XOR 0 = 1).
• For the fifth bit, XOR is with the fourth bit in the binary code (1 XOR 1 = 0).
• So, the Gray code 01101 is indeed correct for the binary code 01001.

Example:

Let's take an example to illustrate how to convert gray code to binary code in C++.

#include <iostream>

#include <bitset>

using namespace std;

// Function to convert Gray code to binary code

int grayToBinary(int gray)

{

 int binary = gray;

 while(gray >>= 1) {

 binary ^= gray;

 }

 return binary;

}

int main() {

 int grayCode1 = 11; // Replace with any Gray code

 int grayCode2 = 7; // Replace with another Gray code

 int binaryCode1 = grayToBinary(grayCode1);

 int binaryCode2 = grayToBinary(grayCode2);

 cout << "Gray code 1: " << grayCode1 << " -> Binary code 1: " << bitset<8>(binaryCode1) << endl;

 cout << "Gray code 2: " << grayCode2 << " -> Binary code 2: " << bitset<8>(binaryCode2) << endl;

 return 0;

}

Output:

Gray code 1: 11 -> Binary code 1: 00001101

Gray code 2: 7 -> Binary code 2: 00000101

Explanation:

• Include Headers: The C++ standard library headers are included at the start of the code. Input and output are handled by iostream, and binary values with leading zeros are shown using bitset.
• Function to Convert Grey to Binary:
• The grayToBinary function is defined to convert Grey code to Binary code.
• The grey code that has to be converted is represented by an integer grey that is entered.
• By using the Grey code, the function initializes an integer binary.
• Next, by XORing binary with the shifted grey value, iteratively performs the Gray-to-Binary conversion using a while loop.
• The resulting binary value is the corresponding binary code, and the loop is repeated until grey reaches zero.
• Principal Purpose:

Two Grey Code values (grayCode1 and grayCode2) are defined in the main function. You can convert any Grey code you want to use in place of these values.

• Conversion and Output:
• The program runs the grayToBinary function for both grayCode1 and grayCode2 to save the binary counterparts in binaryCode1 and binaryCode2.
• Subsequently, the original Grey codes and their equivalent binary codes are displayed using cout.
• The binary form is shown as an 8-bit number with leading zeros when bitset<8> is used. The amount of bits can be changed as needed.

Conclusion:

The C++ code that is provided provides a workable way to translate Grey code to binary code. The function grayToBinary, defined in the code, iteratively converts a Grey code into its corresponding binary representation by using a bitwise XOR operation. Different Grey code values can be entered into the main function, and it will produce the matching binary codes. This code is helpful for a variety of applications where converting grey code is necessary because it is flexible and simple to modify. For a variety of uses in digital electronics, telecommunications, and computer science, among other fields, you can effectively execute Gray-to-Binary conversions by changing the Grey code values in the program.