Binary Code of a number is the representation of a number in Binary (base-2) number system. In Binary Number System, each number is expressed using only two literals (0 and 1). Each of these literals is called a bit. The binary number system is very useful in digital electronic circuits.
Gray Code of a number is the representation of a number using binary literals. But the difference between Binary code and Gray code is that in Gray code, every pair of consecutive numbers differ only by one bit. Gray codes are very useful for the implementation of K-Maps and error correction.
Example:
Binary -> 0100 Gray -> 0110
Binary -> 0101 Gray -> 0111
A Gray code can be converted into a Binary code and vice versa.
Binary to Gray Conversion:
A Binary code can be converted into its equivalent Gray code as:
- The MSB(Most Significant Bit) of the Binary code will be the MSB of the equivalent Gray code.
- All the remaining bits are obtained by performing the XOR operation on the bit at that position with the bit at the previous position in the binary string.
Example:
Binary -> 0011010101
0 XOR 0 XOR 1 XOR 1 XOR 0 XOR 1 XOR 0 XOR 1 XOR 0 XOR 1
↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓
Gray -> 0 0 1 0 1 1 1 1 1 1
Binary -> 0100110
Gray -> 0110101
Code 1:
We use ‘^’ to perform the Xor operation by converting the string to an integer value using Integer.parseInt() function and then performing xor n them.
Java
// Java program to demonstrate Binary// to Gray conversionimport java.io.*;// Classclass GFG { // converts the given binary string into its equivalent // gray code public static void toGray(String binary) { // a String variable to store the obtained gray // string. // the MSB of the gray code is the same as // the MSB of the binary string, i.e., binary[0] String gray = new String(); gray += binary.charAt(0); for (int i = 1; i < binary.length(); i++) { // perform XOR on the previous bit and the // current bit of the binary string gray += (Integer.parseInt(String.valueOf( binary.charAt(i - 1))) ^ Integer.parseInt( String.valueOf(binary.charAt(i)))); } System.out.println("The gray code of " + binary + " is : " + gray); } // Main driver method public static void main(String[] args) { // a String variable to store the given binary // string String binary = "0011010101"; toGray(binary); }} |
The gray code of 0011010101 is : 0010111111
Time complexity: O(n)
Auxiliary space: O(n)
Code 2:
We make a separate user-defined function named xOR(char a, char b) which returns us the xor of two numbers a and b.
Java
// Java program to demonstrate Binary// to Gray conversionimport java.io.*;class GFG { // an auxiliary method to perform XOR on two given // literals public static int xOR(char a, char b) { // return 1 if both bits are not same if (a != b) return 1; // else return 0 return 0; } // converts the given binary string into its equivalent // gray code public static void toGray(String binary) { String gray = new String(); gray += binary.charAt(0); // for all the other bits, traverse through the // binary string for (int i = 1; i < binary.length(); i++) { // calling xOR() method on the previous bit and // the current bit of the binary string gray += xOR(binary.charAt(i - 1), binary.charAt(i)); } System.out.println("The gray code of " + binary + " is : " + gray); } // Driver method public static void main(String[] args) { // a String variable to store the given binary // string String binary = "0011010101"; toGray(binary); }} |
The gray code of 0011010101 is : 0010111111
Time complexity: O(n) where n is length of input string of binary code.
Auxiliary space: O(n) because extra space for String gray is being used
