Comparing leading zeros in binary representations of two numbers

Last Updated : 28 Apr, 2021

Given two integer numbers x and y. Compare and print which one of them has more leading zeros using Bitwise operation. If both the no. have the same no. of leading zeros, print “Equal”.
Note:- A leading zero is any 0 digit that comes before the first nonzero digit in the binary notation of the number.
Examples:

Input : 10, 16
Output :10
Explanation: If we represent the no.s using 8 bit only then 
Binary(10) = 00001010
Binary(16) = 00010000
Clearly, 10 has 4 leading zeros and 16 has 3 leading zeros

Input : 10, 12
Output : Equal
Binary(10) = 00001010
Binary(12) = 00001100
Both have equal no. of leading zeros.

Solution 1: The Naive approach is to first find the binary representation of the numbers and then count the no. of leading zeros.
Solution 2: Find largest power of twos smaller than given numbers, and compare these powers of twos to decide answer.
Solution 3: An efficient approach is to bitwise XOR and AND operators.

Case 1: If both have same no. of leading zeros then (x^y) <= (x & y) because same number of leading 0s would cause a 1 at higher position in x & y.
Case 2 : If we do negation of y and do bitwise AND with x, we get a one at higher position than in y when y has more number of leading 0s.
Case 3: Else x has more leading zeros

C++

// CPP program to find the number with more
// leading zeroes.
#include <bits/stdc++.h>
using namespace std;
 
// Function to compare the no. of leading zeros
void LeadingZeros(int x, int y)
{
    // if both have same no. of leading zeros
    if ((x ^ y) <= (x & y))
        cout << "\nEqual";
 
    // if y has more leading zeros
    else if ((x & (~y)) > y)
        cout << y;
 
    else
        cout << x;
}
 
// Main Function
int main()
{
    int x = 10, y = 16;
    LeadingZeros(x, y);
    return 0;
}

Java

// Java program to find the number
// with more leading zeroes.
class GFG
{
// Function to compare the no.
// of leading zeros
static void LeadingZeros(int x, int y)
{
    // if both have same no. of
    // leading zeros
    if ((x ^ y) <= (x & y))
        System.out.print("\nEqual");
 
    // if y has more leading zeros
    else if ((x & (~y)) > y)
        System.out.print(y);
 
    else
        System.out.print(x);
}
 
// Driver Code
public static void main (String[] args)
{
    int x = 10, y = 16;
    LeadingZeros(x, y);
}
}
 
// This code is contributed by Smitha

Python3

# Python 3 program to find the number
# with more leading zeroes.
 
# Function to compare the no. of
# leading zeros
def LeadingZeros(x, y):
     
    # if both have same no. of
    # leading zeros
    if ((x ^ y) <= (x & y)):
        print("Equal")
 
    # if y has more leading zeros
    elif ((x & (~y)) > y) :
        print(y)
 
    else:
        print(x)
 
# Driver Code
if __name__ == '__main__':
    x = 10
    y = 16
    LeadingZeros(x, y)
 
# This code is contributed
# by Surendra_Gangwar

C#

// C# program to find the number
// with more leading zeroes.
using System;
 
class GFG
{
// Function to compare the no.
// of leading zeros
static void LeadingZeros(int x, int y)
{
    // if both have same no. of
    // leading zeros
    if ((x ^ y) <= (x & y))
        Console.WriteLine("\nEqual");
 
    // if y has more leading zeros
    else if ((x & (~y)) > y)
        Console.WriteLine(y);
 
    else
        Console.WriteLine(x);
}
 
// Driver Code
static public void Main ()
{
    int x = 10, y = 16;
    LeadingZeros(x, y);
}
}
 
// This code is contributed by ajit

PHP

<?php
// PHP program to find the number
// with more leading zeroes.
 
// Function to compare the no.
// of leading zeros
function LeadingZeros($x, $y)
{
    // if both have same no. of
    // leading zeros
    if (($x ^ $y) <= ($x & $y))
        echo "\nEqual";
 
    // if y has more leading zeros
    else if (($x & (~$y)) > $y)
        echo $y;
 
    else
        echo $x;
}
 
// Driver Code
$x = 10;
$y = 16;
LeadingZeros($x, $y);
     
// This code is contributed by ajit
?>

Javascript

<script>
 
// Javascript program to find the number with more
// leading zeroes.
 
// Function to compare the no. of leading zeros
function LeadingZeros(x, y)
{
    // if both have same no. of leading zeros
    if ((x ^ y) <= (x & y))
        document.write("<br>Equal");
 
    // if y has more leading zeros
    else if ((x & (~y)) > y)
        document.write(y);
 
    else
        document.write(x);
}
 
// Main Function
    let x = 10, y = 16;
    LeadingZeros(x, y);
 
</script>

Output:

Time Complexity: O(1)
Space Complexity: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer DSA Live Classes

My Personal Notes

Related Articles

C++

Java

Python3

C#

PHP

Javascript