Even Number: A number which is divisible by 2 and generates a remainder of 0 is called an even number. All the numbers ending with 0, 2, 4, 6, and 8 are even numbers.
Odd Number: An number that is not divisible by 2 and generates a remainder of 1 is called an odd number. All the numbers ending with 1, 3, 5,7, and 9 are odd numbers.
Generic Illustration for any random integer, check whether it is even or odd
Input : 13 Output: ODD Input : 24 Output: EVEN
There are various ways to check whether the given number is odd or even. Some of them are as follows starting from the brute force approach ending up at the most optimal approach.
- Using Brute Force– Naive Approach
- Using Bitwise OR
- Using Bitwise AND
- Using Bitwise XOR
1. Brute Force Naive Approach: It is to check the remainder after dividing by 2. Numbers that are divisible by 2 are even else odd.
Naive Approach is implemented as below:
Java
// Java Program to Check if // a Given Integer is Odd or Even // Importing Classes/Files import java.io.*; import java.util.Scanner; class GFG { // Main Driver Method public static void main(String[] args) { // Declare the integer variable int num = 10; // If condition to check if the remainder is zero if (num % 2 == 0) { // If remainder is zero then this number is even System.out.println("Entered Number is Even"); } else { // If remainder is not zero then this number is // odd System.out.println("Entered Number is Odd"); } } } |
Output:
Entered Number is Even
A Better Approach is to use Bitwise Operators
- Bitwise OR
- Bitwise AND or Bitwise XOR
2. Using Bitwise OR: Bitwise OR operation of the even number by 1 increment the value of the number by 1 otherwise it remains unchanged.
Illustration for Bitwise OR followed by implementation:
Case 1:
Number = 12 1 1 0 0 - Representation of 12 in Binary Format
Bitwise OR 0 0 0 1 - Representation of 1 in Binary Format
1 1 0 1 - Representation of 13 in Binary Format
Result- Number was even so bitwise Or by 1 increment the value by 1
Case 2:
Number = 15 1 1 1 1 - Representation of 15 in Binary Format
Bitwise OR 0 0 0 1 - Representation of 1 in Binary Format
1 1 1 1 - Representation of 15 in Binary Format
Result- Number was odd so bitwise Or by 1 doesn't increment the value by 1
Java
// Java Program to Check if // a Given Integer is Odd or Even // Importing Classes/Files import java.util.*; public class GFG { // Driver Main code public static void main(String[] args) { // Variable to be checked int n = 100; // Condition check // if n|1 if greater than n then this number is even if ((n | 1) > n) { System.out.println("Number is Even"); } else { System.out.println("Number is Odd"); } } } |
Number is Even
3. Using Bitwise AND: Bitwise AND operation of the odd number by 1 will be 1 because the last bit will be already set otherwise it will give 0.
Illustration for Bitwise AND followed by implementation:
Case 1:
Number = 5 0 1 0 1 - Representation of 5 in Binary Format
Bitwise AND 0 0 0 1 - Representation of 1 in Binary Format
0 0 0 1 - Representation of 1 in Binary Format
Result- Number was odd so bitwise And by 1 is 1
Case 2:
Number = 8 1 0 0 0 - Representation of 8 in Binary Format
Bitwise AND 0 0 0 1 - Representation of 1 in Binary Format
0 0 0 0 - Representation of 0 in Binary Format
Result- Number was even so bitwise And by 1 is 0
Java
// Java Program to Check if // a Given Integer is Odd or Even // Importing Classes/Files import java.util.*; public class GFG { // Driver Main Method public static void main(String[] args) { // Declare variable int n = 91; // Condition Check // Bitwise AND of any odd number by 1 gives 1 if ((n & 1) == 1) { System.out.println("Number is Odd"); } else { System.out.println("Number is Even"); } } } |
Number is Odd
4. Using Bitwise XOR: Bitwise XOR operation of the even number by 1 increment the value of the number by 1 otherwise it decrements the value of the number by 1 if the value is odd. It is the most optimal approach.
Illustration for Bitwise XOR followed by implementation:
Case 1:
Number = 5 0 1 0 1 - Representation of 5 in Binary Format
Bitwise XOR 0 0 0 1 - Representation of 1 in Binary Format
0 1 0 0 - Representation of 4 in Binary Format
Result- Number was odd so bitwise And by 1 decrement the value
Case 2:
Number = 8 1 0 0 0 - Representation of 8 in Binary Format
Bitwise XOR 0 0 0 1 - Representation of 1 in Binary Format
1 0 0 1 - Representation of 9 in Binary Format
Result- Number was even so bitwise And by 1 increment the value
Java
// Java Program to Check if // a Given Integer is Odd or Even // Importing Classes/Files import java.util.*; public class GFG { // Driver Main Method public static void main(String[] args) { // Declare Variable int num = 99; // Condition Check // if number^1 increments by 1 then its even number, // else odd if ((num ^ 1) == num + 1) { System.out.println("Number is Even"); } else { System.out.println("Number is Odd"); } } } |
Number is Odd
Attention reader! Don’t stop learning now. Get hold of all the important Java Foundation and Collections concepts with the Fundamentals of Java and Java Collections Course at a student-friendly price and become industry ready.
