Binary Number is the default way to store numbers, but in many applications, binary numbers are difficult to use and a variety of binary numbers is needed. This is where Gray codes are very useful.
Gray code has a property that two successive numbers differ in only one bit because of this property gray code does the cycling through various states with minimal effort and is used in K-maps, error correction, communication, etc.
How to generate n bit Gray Codes?
Following is 2-bit sequence (n = 2) 00 01 11 10 Following is 3-bit sequence (n = 3) 000 001 011 010 110 111 101 100 And Following is 4-bit sequence (n = 4) 0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 1011 1001 1000
n-bit Gray Codes can be generated from a list of (n-1)-bit Gray codes using the following steps.
- Let the list of (n-1)-bit Gray codes be L1. Create another list L2 which is the reverse of L1.
- Modify the list L1 by prefixing a ‘0’ in all codes of L1.
- Modify the list L2 by prefixing a ‘1’ in all codes of L2.
- Concatenate L1 and L2. The concatenated list is the required list of n-bit Gray codes.
Please refer Generate n-bit Gray Codes for a detailed program.
How to Convert Binary To Gray and Vice Versa?
Binary : 0011 Gray : 0010 Binary : 01001 Gray : 01101
In computer science many a time we need to convert binary code to gray code and vice versa. This conversion can be done by applying the following rules :
Binary to Gray conversion :
- The Most Significant Bit (MSB) of the gray code is always equal to the MSB of the given binary code.
- Other bits of the output gray code can be obtained by XORing binary code bit at that index and previous index.
Binary code to gray code conversion
Gray to binary conversion :
- The Most Significant Bit (MSB) of the binary code is always equal to the MSB of the given gray code.
- Other bits of the output binary code can be obtained by checking the gray code bit at that index. If the current gray code bit is 0, then copy the previous binary code bit, else copy the invert of the previous binary code bit.
Gray code to binary code conversion
Below is the implementation of the above steps.
C++
// C++ program for Binary To Gray// and Gray to Binary conversion#include <iostream>using namespace std;// Helper function to xor two characterschar xor_c(char a, char b) { return (a == b) ? '0' : '1'; }// Helper function to flip the bitchar flip(char c) { return (c == '0') ? '1' : '0'; }// function to convert binary string// to gray stringstring binarytoGray(string binary){ string gray = ""; // MSB of gray code is same as binary code gray += binary[0]; // Compute remaining bits, next bit is computed by // doing XOR of previous and current in Binary for (int i = 1; i < binary.length(); i++) { // Concatenate XOR of previous bit // with current bit gray += xor_c(binary[i - 1], binary[i]); } return gray;}// function to convert gray code string// to binary stringstring graytoBinary(string gray){ string binary = ""; // MSB of binary code is same as gray code binary += gray[0]; // Compute remaining bits for (int i = 1; i < gray.length(); i++) { // If current bit is 0, concatenate // previous bit if (gray[i] == '0') binary += binary[i - 1]; // Else, concatenate invert of // previous bit else binary += flip(binary[i - 1]); } return binary;}// Driver program to test above functionsint main(){ string binary = "01001"; cout << "Gray code of " << binary << " is " << binarytoGray(binary) << endl; string gray = "01101"; cout << "Binary code of " << gray << " is " << graytoBinary(gray) << endl; return 0;} |
Java
// Java program for Binary To Gray// and Gray to Binary conversionimport java.io.*;class code_conversion { // Helper function to xor // two characters char xor_c(char a, char b) { return (a == b) ? '0' : '1'; } // Helper function to flip the bit char flip(char c) { return (c == '0') ? '1' : '0'; } // function to convert binary // string to gray string String binarytoGray(String binary) { String gray = ""; // MSB of gray code is same // as binary code gray += binary.charAt(0); // Compute remaining bits, next bit is // computed by doing XOR of previous // and current in Binary for (int i = 1; i < binary.length(); i++) { // Concatenate XOR of previous bit // with current bit gray += xor_c(binary.charAt(i - 1), binary.charAt(i)); } return gray; } // function to convert gray code // string to binary string String graytoBinary(String gray) { String binary = ""; // MSB of binary code is same // as gray code binary += gray.charAt(0); // Compute remaining bits for (int i = 1; i < gray.length(); i++) { // If current bit is 0, // concatenate previous bit if (gray.charAt(i) == '0') binary += binary.charAt(i - 1); // Else, concatenate invert of // previous bit else binary += flip(binary.charAt(i - 1)); } return binary; } // Driver program to test above functions public static void main(String args[]) throws IOException { code_conversion ob = new code_conversion(); String binary = "01001"; System.out.println("Gray code of " + binary + " is " + ob.binarytoGray(binary)); String gray = "01101"; System.out.println("Binary code of " + gray + " is " + ob.graytoBinary(gray)); } }// This code is contributed by Anshika Goyal. |
Python3
# Python3 program for Binary To Gray# and Gray to Binary conversion# Helper function to xor two charactersdef xor_c(a, b): return '0' if(a == b) else '1';# Helper function to flip the bitdef flip(c): return '1' if(c == '0') else '0';# function to convert binary string# to gray stringdef binarytoGray(binary): gray = ""; # MSB of gray code is same as # binary code gray += binary[0]; # Compute remaining bits, next bit # is computed by doing XOR of previous # and current in Binary for i in range(1, len(binary)): # Concatenate XOR of previous # bit with current bit gray += xor_c(binary[i - 1], binary[i]); return gray;# function to convert gray code# string to binary stringdef graytoBinary(gray): binary = ""; # MSB of binary code is same # as gray code binary += gray[0]; # Compute remaining bits for i in range(1, len(gray)): # If current bit is 0, # concatenate previous bit if (gray[i] == '0'): binary += binary[i - 1]; # Else, concatenate invert # of previous bit else: binary += flip(binary[i - 1]); return binary;# Driver Codebinary = "01001";print("Gray code of", binary, "is", binarytoGray(binary));gray = "01101";print("Binary code of", gray, "is", graytoBinary(gray)); # This code is contributed by mits |
C#
// C# program for Binary To Gray// and Gray to Binary conversion.using System;class GFG { // Helper function to xor // two characters static char xor_c(char a, char b) { return (a == b) ? '0' : '1'; } // Helper function to flip the bit static char flip(char c) { return (c == '0') ? '1' : '0'; } // function to convert binary // string to gray string static String binarytoGray(String binary) { String gray = ""; // MSB of gray code is same // as binary code gray += binary[0]; // Compute remaining bits, next // bit is computed by doing XOR // of previous and current in // Binary for (int i = 1; i < binary.Length; i++) { // Concatenate XOR of previous // bit with current bit gray += xor_c(binary[i - 1], binary[i]); } return gray; } // function to convert gray code // string to binary string static String graytoBinary(String gray) { String binary = ""; // MSB of binary code is same // as gray code binary += gray[0]; // Compute remaining bits for (int i = 1; i < gray.Length; i++) { // If current bit is 0, // concatenate previous bit if (gray[i] == '0') binary += binary[i - 1]; // Else, concatenate invert of // previous bit else binary += flip(binary[i - 1]); } return binary; } // Driver program to test above // functions public static void Main() { String binary = "01001"; Console.WriteLine("Gray code of " + binary + " is " + binarytoGray(binary)); String gray = "01101"; Console.Write("Binary code of " + gray + " is " + graytoBinary(gray)); }}// This code is contributed by nitin mittal. |
PHP
<?php// PHP program for Binary To Gray// and Gray to Binary conversion// Helper function to xor two charactersfunction xor_c($a, $b) { return ($a == $b) ? '0' : '1'; }// Helper function to flip the bitfunction flip($c) { return ($c == '0') ? '1' : '0'; }// function to convert binary string// to gray stringfunction binarytoGray($binary){ $gray = ""; // MSB of gray code is same as // binary code $gray .= $binary[0]; // Compute remaining bits, next bit is // computed by doing XOR of previous // and current in Binary for ($i = 1; $i < strlen($binary); $i++) { // Concatenate XOR of previous bit // with current bit $gray .= xor_c($binary[$i - 1], $binary[$i]); } return $gray;}// function to convert gray code string// to binary stringfunction graytoBinary($gray){ $binary = ""; // MSB of binary code is same as gray code $binary .= $gray[0]; // Compute remaining bits for ($i = 1; $i < strlen($gray); $i++) { // If current bit is 0, concatenate // previous bit if ($gray[$i] == '0') $binary .= $binary[$i - 1]; // Else, concatenate invert of // previous bit else $binary .= flip($binary[$i - 1]); } return $binary;}// Driver Code$binary = "01001";print("Gray code of " . $binary . " is " . binarytoGray($binary) . "\n");$gray = "01101";print("Binary code of " . $gray . " is " . graytoBinary($gray)); // This code is contributed by mits?> |
Javascript
<script> // Javascript program for Binary To Gray// and Gray to Binary conversion// Helper function to xor two charactersfunction xor_c(a, b){ return (a == b) ? '0' : '1'; }// Helper function to flip the bitfunction flip(c){ return (c == '0') ? '1' : '0'; }// Function to convert binary string// to gray stringfunction binarytoGray(binary){ let gray = ""; // MSB of gray code is same // as binary code gray += binary[0]; // Compute remaining bits, next bit // is computed by doing XOR of previous // and current in Binary for(let i = 1; i < binary.length; i++) { // Concatenate XOR of previous bit // with current bit gray += xor_c(binary[i - 1], binary[i]); } return gray;}// Function to convert gray code string// to binary stringfunction graytoBinary(gray){ let binary = ""; // MSB of binary code is same // as gray code binary += gray[0]; // Compute remaining bits for(let i = 1; i < gray.length; i++) { // If current bit is 0, concatenate // previous bit if (gray[i] == '0') binary += binary[i - 1]; // Else, concatenate invert of // previous bit else binary += flip(binary[i - 1]); } return binary;}// Driver codelet binary = "01001";document.write("Gray code of " + binary + " is " + binarytoGray(binary) + "</br>");let gray = "01101";document.write("Binary code of " + gray + " is " + graytoBinary(gray)); // This code is contributed by vaibhavrabadiya3</script> |
Output
Gray code of 01001 is 01101 Binary code of 01101 is 01001
Time Complexity: O(n)
Auxiliary Space: O(n)
Here, n is length of the binary string.
Binary to Gray using Bitwise Operators
C++
// C++ program for above approach#include <bits/stdc++.h>using namespace std;int greyConverter(int n) { return n ^ (n >> 1); }int main(){ int n = 3; cout << greyConverter(n) << endl; n = 9; cout << greyConverter(n) << endl; return 0;} |
Java
// Java Program for above approachpublic class Main { public static int greyConverter(int n) { return n ^ (n >> 1); } // Driver code public static void main(String[] args) { int n = 3; System.out.println(greyConverter(n)); n = 9; System.out.println(greyConverter(n)); }}// This code is contributed by divyesh072019 |
Python3
# Python3 code for above approachdef greyConverter(n): return n ^ (n >> 1)n = 3print(greyConverter(n))n = 9print(greyConverter(n))# This code is contributed by divyeshrabadiya07 |
C#
// C# program for above approachusing System;class GFG { static int greyConverter(int n) { return n ^ (n >> 1); } // Driver Code public static void Main(string[] args) { int n = 3; Console.WriteLine(greyConverter(n)); n = 9; Console.WriteLine(greyConverter(n)); }}// This code is contributed by rutvik_56 |
Javascript
<script>// Javascript program for above approachfunction greyConverter(n) { return n ^ (n >> 1); }// Driver codelet n = 3;document.write(greyConverter(n) + "</br>");n = 9;document.write(greyConverter(n));// This code is contributed by suresh07</script> |
Output
2 13
Time Complexity: O(1)
Auxiliary Space: O(1)
Gray to Binary using Bitwise Operators
C++
// C++ program for above approach#include <bits/stdc++.h>using namespace std;int binaryConverter(int n){ int res = n; while (n > 0) { n >>= 1; res ^= n; } return res;}// Driver Codeint main(){ int n = 4; // Function call cout << binaryConverter(n) << endl; return 0;}// This code is contributed by sshrey47 |
Java
// Java Program for above approachpublic class Main { public static int binaryConverter(int n) { int res = n; while (n > 0) { n >>= 1; res ^= n; } return res; } // Driver code public static void main(String[] args) { int n = 4; System.out.println(binaryConverter(n)); }}// This code is contributed by sshrey47 |
Python3
# Python3 code for above approachdef binaryConverter(n): res = n while n > 0: n >>= 1 res ^= n return resn = 4print(binaryConverter(n))# This code is contributed by sshrey47 |
C#
using System;public class GFG { static int binaryConverter(int n) { int res = n; while (n > 0) { n >>= 1; res ^= n; } return res; } static public void Main() { int n = 4; Console.WriteLine(binaryConverter(n)); }}// This code is contributed by sshrey47 |
Javascript
<script> // Javascript program for above approach function binaryConverter(n) { let res = n; while (n > 0) { n >>= 1; res ^= n; } return res; } let n = 4; // Function call document.write(binaryConverter(n)); // This code is contributed by mukesh07.</script> |
Output
7
Time Complexity: O(log(n))
Auxiliary Space: O(1)
This article is contributed by Utkarsh Trivedi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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