Check a number is even or odd without using arithmetic operators

The given problem is to determine whether a given number is even or odd without using any arithmetic operators (e.g., modulo, division, etc.). We need to come up with a solution that relies on bitwise operations instead of conventional arithmetic calculations.

Explanation with Suitable Example

Let's understand the approach through an example. Consider the number 18 in binary representation:

18 (Decimal) = 10010 (Binary)

To determine if this number is even or odd using bitwise operations, we can use the fact that even numbers have their least significant bit (LSB) set to 0, while odd numbers have their LSB set to 1. The LSB is the rightmost bit of a binary representation.

Pseudocode

1. Read the input number num.
2. Perform a bitwise AND operation between num and 1 (binary representation: 0001).
3. If the result of the bitwise AND is 0, then the number is even. Otherwise, it is odd.
4. Print the result accordingly.

Algorithm

checkEvenOdd(num):
    if (num & 1) is 0:
        print "Is Even Number"
    else:
        print "Is Odd Number"

Explanation

1. We take the input number num.
2. We perform a bitwise AND operation between num and 1 (num & 1).
3. The bitwise AND operation will only preserve the LSB of num and set all other bits to 0.
4. If the result of the bitwise AND operation is 0, it means the LSB of num is 0, indicating that the number is even. In this case, we print "Is Even Number".
5. If the result of the bitwise AND operation is 1, it means the LSB of num is 1, indicating that the number is odd. In this case, we print "Is Odd Number".

Code Solution

• C
• Java
• C++
• C#
• Php
• Node Js
• Python
• Ruby
• Scala
• Swift 4
• Kotlin
• Rust

// C Program 
// Check a number is even or odd without using arithmetic operators
#include <stdio.h>
// Determine whether given number is Even or Odd
void checkEvenOdd(int num)
{
    // Display given number
    printf("\n Number : %d",num);

    if((num & 1 ) == 0 )
    {
        // When last bit is not set
        printf("\n Is Even Number \n");
    }
    else
    {
        printf("\n Is Odd Number\n");
    }
}
int main(int argc, char const *argv[])
{

    // Test Cases
    // 12 (1100)
    checkEvenOdd(12);
    // 34 (100010)
    checkEvenOdd(34);
    // -12 (∞11110100)
    checkEvenOdd(-12);
    // 7 (111)
    checkEvenOdd(7);
    // 21 (00010101)
    checkEvenOdd(21);
    // -11 (11110101)
    checkEvenOdd(-11);
    return 0;
}

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

/*
  Java Program 
  Check a number is even or odd without using arithmetic operators
*/
public class Comparison
{
    // Determine whether given number is Even or Odd
    public void checkEvenOdd(int num)
    {
        // Display given number
        System.out.print("\n Number : " + num );
        if ((num & 1) == 0)
        {
            // When last bit is not set
            System.out.print("\n Is Even Number \n");
        }
        else
        {
            System.out.print("\n Is Odd Number\n");
        }
    }
    public static void main(String[] args)
    {
        Comparison task = new Comparison();
        // Test Cases
        // 12 (1100)
        task.checkEvenOdd(12);
        // 34 (100010)
        task.checkEvenOdd(34);
        // -12 (∞11110100)
        task.checkEvenOdd(-12);
        // 7 (111)
        task.checkEvenOdd(7);
        // 21 (00010101)
        task.checkEvenOdd(21);
        // -11 (11110101)
        task.checkEvenOdd(-11);
    }
}

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

// Include header file
#include <iostream>
using namespace std;
/*
  C++ Program 
  Check a number is even or odd without using arithmetic operators
*/
class Comparison
{
	public:
		// Determine whether given number is Even or Odd
		void checkEvenOdd(int num)
		{
			// Display given number
			cout << "\n Number : " << num;
			if ((num &1) == 0)
			{
				// When last bit is not set
				cout << "\n Is Even Number \n";
			}
			else
			{
				cout << "\n Is Odd Number\n";
			}
		}
};
int main()
{
	Comparison task = Comparison();
	// Test Cases
	// 12 (1100)
	task.checkEvenOdd(12);
	// 34 (100010)
	task.checkEvenOdd(34);
	// -12 (∞11110100)
	task.checkEvenOdd(-12);
	// 7 (111)
	task.checkEvenOdd(7);
	// 21 (00010101)
	task.checkEvenOdd(21);
	// -11 (11110101)
	task.checkEvenOdd(-11);
	return 0;
}

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

// Include namespace system
using System;
/*
  C# Program 
  Check a number is even or odd without using arithmetic operators
*/
public class Comparison
{
	// Determine whether given number is Even or Odd
	public void checkEvenOdd(int num)
	{
		// Display given number
		Console.Write("\n Number : " + num);
		if ((num & 1) == 0)
		{
			// When last bit is not set
			Console.Write("\n Is Even Number \n");
		}
		else
		{
			Console.Write("\n Is Odd Number\n");
		}
	}
	public static void Main(String[] args)
	{
		Comparison task = new Comparison();
		// Test Cases
		// 12 (1100)
		task.checkEvenOdd(12);
		// 34 (100010)
		task.checkEvenOdd(34);
		// -12 (∞11110100)
		task.checkEvenOdd(-12);
		// 7 (111)
		task.checkEvenOdd(7);
		// 21 (00010101)
		task.checkEvenOdd(21);
		// -11 (11110101)
		task.checkEvenOdd(-11);
	}
}

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

<?php
/*
  Php Program 
  Check a number is even or odd without using arithmetic operators
*/
class Comparison
{
	// Determine whether given number is Even or Odd
	public	function checkEvenOdd($num)
	{
		// Display given number
		echo "\n Number : ". $num;
		if (($num & 1) == 0)
		{
			// When last bit is not set
			echo "\n Is Even Number \n";
		}
		else
		{
			echo "\n Is Odd Number\n";
		}
	}
}

function main()
{
	$task = new Comparison();
	// Test Cases
	// 12 (1100)
	$task->checkEvenOdd(12);
	// 34 (100010)
	$task->checkEvenOdd(34);
	// -12 (∞11110100)
	$task->checkEvenOdd(-12);
	// 7 (111)
	$task->checkEvenOdd(7);
	// 21 (00010101)
	$task->checkEvenOdd(21);
	// -11 (11110101)
	$task->checkEvenOdd(-11);
}
main();

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

/*
  Node Js Program 
  Check a number is even or odd without using arithmetic operators
*/
class Comparison
{
	// Determine whether given number is Even or Odd
	checkEvenOdd(num)
	{
		// Display given number
		process.stdout.write("\n Number : " + num);
		if ((num & 1) == 0)
		{
			// When last bit is not set
			process.stdout.write("\n Is Even Number \n");
		}
		else
		{
			process.stdout.write("\n Is Odd Number\n");
		}
	}
}

function main()
{
	var task = new Comparison();
	// Test Cases
	// 12 (1100)
	task.checkEvenOdd(12);
	// 34 (100010)
	task.checkEvenOdd(34);
	// -12 (∞11110100)
	task.checkEvenOdd(-12);
	// 7 (111)
	task.checkEvenOdd(7);
	// 21 (00010101)
	task.checkEvenOdd(21);
	// -11 (11110101)
	task.checkEvenOdd(-11);
}
main();

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

#   Python 3 Program 
#   Check a number is even or odd without using arithmetic operators

class Comparison :
	#  Determine whether given number is Even or Odd
	def checkEvenOdd(self, num) :
		#  Display given number
		print("\n Number : ", num, end = "")
		if ((num & 1) == 0) :
			#  When last bit is not set
			print("\n Is Even Number ")
		else :
			print("\n Is Odd Number")
		
	

def main() :
	task = Comparison()
	#  Test Cases
	#  12 (1100)
	task.checkEvenOdd(12)
	#  34 (100010)
	task.checkEvenOdd(34)
	#  -12 (∞11110100)
	task.checkEvenOdd(-12)
	#  7 (111)
	task.checkEvenOdd(7)
	#  21 (00010101)
	task.checkEvenOdd(21)
	#  -11 (11110101)
	task.checkEvenOdd(-11)

if __name__ == "__main__": main()

 Number :  12
 Is Even Number

 Number :  34
 Is Even Number

 Number :  -12
 Is Even Number

 Number :  7
 Is Odd Number

 Number :  21
 Is Odd Number

 Number :  -11
 Is Odd Number

#   Ruby Program 
#   Check a number is even or odd without using arithmetic operators

class Comparison 
	#  Determine whether given number is Even or Odd
	def checkEvenOdd(num) 
		#  Display given number
		print("\n Number : ", num)
		if ((num & 1) == 0) 
			#  When last bit is not set
			print("\n Is Even Number \n")
		else 
			print("\n Is Odd Number\n")
		end

	end

end

def main() 
	task = Comparison.new()
	#  Test Cases
	#  12 (1100)
	task.checkEvenOdd(12)
	#  34 (100010)
	task.checkEvenOdd(34)
	#  -12 (∞11110100)
	task.checkEvenOdd(-12)
	#  7 (111)
	task.checkEvenOdd(7)
	#  21 (00010101)
	task.checkEvenOdd(21)
	#  -11 (11110101)
	task.checkEvenOdd(-11)
end

main()

 Number : 12
 Is Even Number 

 Number : 34
 Is Even Number 

 Number : -12
 Is Even Number 

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

/*
  Scala Program 
  Check a number is even or odd without using arithmetic operators
*/
class Comparison
{
	// Determine whether given number is Even or Odd
	def checkEvenOdd(num: Int): Unit = {
		// Display given number
		print("\n Number : " + num);
		if ((num & 1) == 0)
		{
			// When last bit is not set
			print("\n Is Even Number \n");
		}
		else
		{
			print("\n Is Odd Number\n");
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var task: Comparison = new Comparison();
		// Test Cases
		// 12 (1100)
		task.checkEvenOdd(12);
		// 34 (100010)
		task.checkEvenOdd(34);
		// -12 (∞11110100)
		task.checkEvenOdd(-12);
		// 7 (111)
		task.checkEvenOdd(7);
		// 21 (00010101)
		task.checkEvenOdd(21);
		// -11 (11110101)
		task.checkEvenOdd(-11);
	}
}

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

/*
  Swift 4 Program 
  Check a number is even or odd without using arithmetic operators
*/
class Comparison
{
	// Determine whether given number is Even or Odd
	func checkEvenOdd(_ num: Int)
	{
		// Display given number
		print("\n Number : ", num, terminator: "");
		if ((num & 1) == 0)
		{
			// When last bit is not set
			print("\n Is Even Number ");
		}
		else
		{
			print("\n Is Odd Number");
		}
	}
}
func main()
{
	let task: Comparison = Comparison();
	// Test Cases
	// 12 (1100)
	task.checkEvenOdd(12);
	// 34 (100010)
	task.checkEvenOdd(34);
	// -12 (∞11110100)
	task.checkEvenOdd(-12);
	// 7 (111)
	task.checkEvenOdd(7);
	// 21 (00010101)
	task.checkEvenOdd(21);
	// -11 (11110101)
	task.checkEvenOdd(-11);
}
main();

 Number :  12
 Is Even Number

 Number :  34
 Is Even Number

 Number :  -12
 Is Even Number

 Number :  7
 Is Odd Number

 Number :  21
 Is Odd Number

 Number :  -11
 Is Odd Number

/*
  Kotlin Program 
  Check a number is even or odd without using arithmetic operators
*/
class Comparison
{
	// Determine whether given number is Even or Odd
	fun checkEvenOdd(num: Int): Unit
	{
		// Display given number
		print("\n Number : " + num);
		if ((num and 1) == 0)
		{
			// When last bit is not set
			print("\n Is Even Number \n");
		}
		else
		{
			print("\n Is Odd Number\n");
		}
	}
}
fun main(args: Array < String > ): Unit
{
	var task: Comparison = Comparison();
	// Test Cases
	// 12 (1100)
	task.checkEvenOdd(12);
	// 34 (100010)
	task.checkEvenOdd(34);
	// -12 (∞11110100)
	task.checkEvenOdd(-12);
	// 7 (111)
	task.checkEvenOdd(7);
	// 21 (00010101)
	task.checkEvenOdd(21);
	// -11 (11110101)
	task.checkEvenOdd(-11);
}

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

// Rust Program 
// Check a number is even or odd without using arithmetic operators
fn main()
{
	// Test Cases
	// 12 (1100)
	check_even_odd(12);
	// 34 (100010)
	check_even_odd(34);
	// -12 (∞11110100)
	check_even_odd(-12);
	// 7 (111)
	check_even_odd(7);
	// 21 (00010101)
	check_even_odd(21);
	// -11 (11110101)
	check_even_odd(-11);
}
// Determine whether given number is Even or Odd
fn check_even_odd(num: i32)
{
	// Display given number
	print!("\n Number : {}", num);
	if (num & 1) == 0
	{
		// When last bit is not set
		print!("\n Is Even Number \n");
	}
	else
	{
		print!("\n Is Odd Number\n");
	}
}

 Number : 12
 Is Even Number

 Number : 34
 Is Even Number

 Number : -12
 Is Even Number

 Number : 7
 Is Odd Number

 Number : 21
 Is Odd Number

 Number : -11
 Is Odd Number

Resultant Output Explanation

• For the test cases provided in the code:
  1. checkEvenOdd(12) - The binary representation of 12 is 1100, and since the LSB is 0, the number is even. Output: "Is Even Number".
  2. checkEvenOdd(34) - The binary representation of 34 is 100010, and since the LSB is 0, the number is even. Output: "Is Even Number".
  3. checkEvenOdd(-12) - The binary representation of -12 (assuming 8-bit two's complement) is 11110100, and since the LSB is 0, the number is even. Output: "Is Even Number".
  4. checkEvenOdd(7) - The binary representation of 7 is 111, and since the LSB is 1, the number is odd. Output: "Is Odd Number".
  5. checkEvenOdd(21) - The binary representation of 21 is 10101, and since the LSB is 1, the number is odd. Output: "Is Odd Number".
  6. checkEvenOdd(-11) - The binary representation of -11 (assuming 8-bit two's complement) is 11110101, and since the LSB is 1, the number is odd. Output: "Is Odd Number".

Time Complexity of the Code

The time complexity of this code is O(1) because the operations performed are independent of the input size. The bitwise AND operation takes constant time as it is performed on the fixed-size binary representation of the input number. Therefore, the time complexity remains constant regardless of the input magnitude.