Python Count set bits in a range?

A given positive number when converted to binary has a number of set bits. Set bits in a binary number are represented by 1. In this article we will see how to count the number of set bits in a specific range of positions within a binary representation of a number.

Using bin() and String Slicing

In the below example we take a number and apply the bin() function to get the binary value. Then we slice it to remove the prefixes and count set bits in the specified range ?

Example

def SetBits_cnt(n, l, r):
    bin_val = bin(n)
    
    # Remove '0b' prefixed in bin_val conversion
    bin_val = bin_val[2:]
    print("Binary representation:", bin_val)
    
    # reverse string to count from right (LSB)
    bin_val = bin_val[-1::-1]
    
    # count all set bit '1' starting from index l-1 to r-1
    count = len([bin_val[i] for i in range(l - 1, r) if i < len(bin_val) and bin_val[i] == '1'])
    print("Set bits in range [{}, {}]:".format(l, r), count)
    return count

SetBits_cnt(83, 1, 6)

Output

Running the above code gives us the following result ?

Binary representation: 1010011
Set bits in range [1, 6]: 3

Using Bitwise Operations

The bitwise operator approach is more efficient. We create a mask to extract bits in the specified range, then count the set bits using Brian Kernighan's algorithm ?

Example

def trackBitsInRange(n, l, r):
    # Create mask using bitwise operator
    mask = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1)
    
    # Extract bits in range and count set bits
    return trackSetBits(n & mask)

def trackSetBits(n):
    count = 0
    while n:
        n &= (n - 1)  # Brian Kernighan's algorithm
        count += 1
    return count

# Example usage
number = 83
left = 1
right = 6

print("Number:", number)
print("Binary:", bin(number))
print("Set bits in range [{}, {}]:".format(left, right), trackBitsInRange(number, left, right))

Output

Running the above code gives us the following result ?

Number: 83
Binary: 0b1010011
Set bits in range [1, 6]: 3

Comparison

How Range Works

In both methods, the range [l, r] represents bit positions from right to left (1-indexed). For number 83 (binary: 1010011):

• Position 1: 1 (rightmost bit)
• Position 2: 1
• Position 3: 0
• Position 4: 0
• Position 5: 1
• Position 6: 0

Range [1, 6] includes positions 1, 2, 3, 4, 5, giving us 3 set bits.

Conclusion

Use the bitwise approach for better performance with O(1) space complexity. The string slicing method is easier to understand but requires more memory for string operations.