JavaScript Program to Find First Set Bit

The rightmost bit in a binary representation of a number that is set to 1 is called the "First Set Bit". It indicates the lowest significant bit where the value changes from 0 to 1.

Examples:

Input: 
N = 18
Output: 
2
Explanation: 
Binary representation of 18 is 010010,the first set bit from the right side is at position 2.

Input: 
N = 12 
Output: 
3 
Explanation: 
Binary representation of  12 is 1100, the first set bit from the right side is at position 3.

Using bitwise AND and shifting

In this approach, we are using the bitwise AND (&) operator with 1 to check each bit of the number from right to left. If a set bit is found, we determine its position by incrementing a counter variable (res) and breaking the loop.

Example: Implementation to use bitwise AND and shifting to find the first set bit.

JavaScript

let num = 18;
let res = 0;
while (num > 0) {
    res++;
    if (num & 1) {
        console.log("Position of first set bit:", res);
        break;
    }
    num >>= 1;
}
if (num === 0) {
    console.log("No set bit found");
}

Output

Position of first set bit: 2

Time Complexity: O(log n)

Auxiliary Space: O(1)

Using logarithm and bitwise right shift

In this approach, we are using bitwise AND (&) with the two's complement of the number to isolate the rightmost set bit. Then, we use the logarithm (base 2) to find its position, accounting for 1-based indexing, to determine the position of the first set bit.

Example: Implementation to use logarithm and bitwise right shift to find the first set bit.

JavaScript

let num = 12;
if (num === 0) {
    console.log("No set bit found");
} else {
    console.log("Position of first set bit:",
        Math.floor(Math.log2(num & -num)) + 1);
}

Output

Position of first set bit: 3

Time Complexity: O(1)

Auxiliary Space: O(1)

Using String Conversion

In this approach, we convert the given number to its binary representation using string conversion. Then, we find the index of the first '1' character in the binary string, representing the position of the first set bit. This method offers simplicity but might be less efficient compared to bitwise operations.

Example: Implementation to use logarithm and bitwise right shift to find the first set bit.

JavaScript

function findFirstSetBitString(number) {
    const binaryString = number.toString(2);
    const firstSetBitIndex =
        binaryString.length - binaryString.indexOf('1');
    return firstSetBitIndex;
}

console.log(findFirstSetBitString(10));

Output

4

Time Complexity: O(log n)

Auxiliary Space: O(log n)

Conclusion

In this article, we explored multiple approaches to finding the position of the first set bit in a number using JavaScript. Depending on the requirements and constraints of your application, you can choose the most suitable approach. While bitwise operations offer efficiency, logarithmic functions provide a concise solution, and string conversion offers simplicity at the cost of performance.