# Comparing leading zeros in binary representations of two numbers

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. has 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.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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

 ` ``\$y``)  ` `        ``echo` `\$y``; ` ` `  `    ``else` `        ``echo` `\$x``; ` `} ` ` `  `// Driver Code ` `\$x` `= 10; ` `\$y` `= 16; ` `LeadingZeros(``\$x``, ``\$y``); ` `     `  `// This code is contributed by ajit ` `?> `

Output:

```10
```

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

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