We are given with an integer array of size N(size of multiple 4) and we have to perform Xclusive OR operation on the array such that input[1- 4] resembles utility_arr[1- 4] and the conditions of computing is If arr[1 – 4] = {a1, a2, a3, a4} then q[1 – 4] = {a1 ⊕ a2 ⊕ a3, a1 ⊕ a2 ⊕ a4, a1 ⊕ a3 ⊕ a4, a2 ⊕ a3 ⊕ a4}
Let us see various input output scenarios for this -
In − int[] input = { 5, 2, 3, 4 };
Out − Result after XOR operation 4 3 2 5
Explanation −An Exclusive-OR gate's output only goes "HIGH" when both of its input terminals are at "DIFFERENT" logic levels from one another. The output is a "0" if these two inputs, A and B, are both at logic level "1" or "0," making the gate a "odd but not the even gate." In other words, when the inputs have an odd number of 1s, the output is "1."
a1 ⊕ a2 ⊕ a3 = 5 ⊕ 2 ⊕ 3 = 4
a1 ⊕ a2 ⊕ a4 = 5 ⊕ 2 ⊕ 4 = 3
a1 ⊕ a3 ⊕ a4 = 5⊕ 3 ⊕ 4 = 2
a2 ⊕ a3 ⊕ a4 = 2 ⊕ 3 ⊕ 4 = 5
In − int[] input = { 7, 6, 4, 4, 3, 8, 9, 5 };
Out − Result after XOR operations 5 5 7 6 2 14 15 4
Explanation − An Exclusive-OR gate's output only goes "HIGH" when both of its input terminals are at "DIFFERENT" logic levels from one another. The output is a "0" if these two inputs, A and B, are both at logic level "1" or "0," making the gate a "odd but not the even gate." In other words, when the inputs have an odd number of 1s, the output is "1." Will only work for input[] of size multiples of 4, other sized input arrays will show 0s in place of odd placed numbers.
Result after XOR operations 5 5 7 6 2 14 15 4
Approach used in the below program is as follows −
According to the properties of XOR a ⊕ a = 0 and a ⊕ 0 = a. (a ⊕ b ⊕ c) ⊕ (b ⊕ c ⊕ d) = a ⊕ d (As (b ⊕ c) ⊕ (b ⊕ c) = 0)
For computation the array is divided into groups of 4 and we will follow the properties of XOR to calculate the results of each group.
Taking reference from the above property using (a ⊕ d) we can calculate b and c (a ⊕ b ⊕ d) ⊕ (a ⊕ d) = b (a ⊕ c ⊕ d) ⊕ (a ⊕ d) = c
And by using b and c we can get a and d by using the following approach (a ⊕ b ⊕ c) ⊕ (b) ⊕ (c) = a (b ⊕ c ⊕ d) ⊕ (b) ⊕ (c) = d
The process is repeated for all four groups
A loop is iterated with 2 pointers i and j till length of the array divided by four and a temp value(ans) and an utility array(which stores answers) is introduced.
Inside the for loop following xor operations are implemented
ans= input array[i] ⊕ input array[i+3]
Utility array[i+1](calculating b)= input array[i+1] ⊕ ans
Utility array[i+2](calculating c)= input array[i+2] ⊕ ans
Utility array[i](calculating a)= input array[i] ⊕ ((Utility array[i + 1]) ^ (Utility array[i + 2]))
Utility array[i](calculating d)= input array[i+3] ⊕ ((Utility array[i + 1]) ^ (Utility array[i + 2]))
And the pointer is updated for next set of four characters
Finally, the array is printed and the result is returned to the user.
Example
import java.util.Arrays;
import java.util.List;
public class Tutorials{
static int ans = 0;
public static void main(String args[]){
int[] input = {7, 1, 2, 3};
int[] arr = new int[input.length];
for (int i = 0, j = 0; j < input.length / 4; j++){
ans = input[i] ^ input[i + 3];
arr[i + 1] = input[i + 1] ^ ans;
arr[i + 2] = input[i + 2] ^ ans;
arr[i] = input[i] ^ ((arr[i + 1]) ^ (arr[i + 2]));
arr[i + 3] = input[i + 3] ^ (arr[i + 1] ^ arr[i + 2]);
i += 4;
}
System.out.println("Different XORs of elements in groups of size 4 is: ");
for (int i = 0; i < arr.length; i++){
System.out.println(arr[i]);
}
}
}Output
If we run the above code it will generate the following Output
Different XORs of elements in groups of size 4 is : 4 5 6 0