C# program to count total set bits in a number

A set bit refers to a bit that has a value of 1 in the binary representation of a number. Counting set bits is a common programming problem that involves examining each bit position to determine how many are set to 1.

For example, the number 11 in decimal has the binary representation 1011, which contains 3 set bits (three 1s).

Approach

The most straightforward approach uses bitwise operations to examine each bit −

• Use the bitwise AND operator (&) with 1 to check if the least significant bit is set

• Right-shift the number by 1 bit to examine the next bit

• Continue until the number becomes 0

Using Bitwise Operations

Example

using System;

public class Demo {
   public static void Main() {
      int count = 0;
      int num = 11; // Binary: 1011
      
      Console.WriteLine("Number: " + num);
      Console.WriteLine("Binary: " + Convert.ToString(num, 2));
      
      while (num > 0) {
         count += num & 1;  // Check if LSB is 1
         num >>= 1;         // Right shift by 1
      }
      
      Console.WriteLine("Total set bits: " + count);
   }
}

The output of the above code is −

Number: 11
Binary: 1011
Total set bits: 3

Using Built-in Method

.NET provides a built-in method PopCount in the BitOperations class for counting set bits −

Example

using System;
using System.Numerics;

public class Demo {
   public static void Main() {
      int num = 11;
      
      Console.WriteLine("Number: " + num);
      Console.WriteLine("Binary: " + Convert.ToString(num, 2));
      
      int setBits = BitOperations.PopCount((uint)num);
      Console.WriteLine("Total set bits: " + setBits);
   }
}

The output of the above code is −

Number: 11
Binary: 1011
Total set bits: 3

Brian Kernighan's Algorithm

This optimized approach eliminates trailing zeros by using the property that n & (n-1) removes the rightmost set bit −

Example

using System;

public class Demo {
   public static void Main() {
      int count = 0;
      int num = 11; // Binary: 1011
      
      Console.WriteLine("Number: " + num);
      Console.WriteLine("Binary: " + Convert.ToString(num, 2));
      
      while (num > 0) {
         count++;
         num = num & (num - 1);  // Remove rightmost set bit
      }
      
      Console.WriteLine("Total set bits: " + count);
   }
}

The output of the above code is −

Number: 11
Binary: 1011
Total set bits: 3

Comparison

Conclusion

Counting set bits can be accomplished using bitwise operations, Brian Kernighan's algorithm for optimization, or built-in methods like BitOperations.PopCount. The choice depends on performance requirements and .NET version compatibility.