# Count of N-bit binary numbers without leading zeros

• Last Updated : 10 Mar, 2022

Given an integer N, the task is to find the count of N-bit binary numbers without leading zeros.
Examples:

Input: N = 2
Output:
10 and 11 are the only possible binary numbers.
Input: N = 4
Output:

Approach: Since the numbers cannot have leading zeros so the left-most bit has to be set to 1. Now for the rest of the N – 1 bits, there are two choices they can either be set to 0 or 1. So, the count of possible numbers will be 2N – 1.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the count``// of possible numbers``int` `count(``int` `n)``{``    ``return` `pow``(2, n - 1);``}` `// Driver code``int` `main()``{``    ``int` `n = 4;` `    ``cout << count(n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{``    ` `    ``// Function to return the count``    ``// of possible numbers``    ``static` `int` `count(``int` `n)``    ``{``        ``return` `(``int``)Math.pow(``2``, n - ``1``);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `n = ``4``;``    ` `        ``System.out.println(count(n));``    ``}``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 implementation of the approach` `# Function to return the count``# of possible numbers``def` `count(n):``    ``return` `pow``(``2``, n ``-` `1``)` `# Driver code``n ``=` `4` `print``(count(n))` `# This code is contributed by mohit kumar`

## C#

 `// C# implementation of the approach``using` `System;``    ` `class` `GFG``{``    ``// Function to return the count``    ``// of possible numbers``    ``static` `int` `count(``int` `n)``    ``{``        ``return` `(``int``)Math.Pow(2, n - 1);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main (String[] args)``    ``{``        ``int` `n = 4;``    ` `        ``Console.WriteLine(count(n));``    ``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`8`

Time Complexity: O(log n)

Auxiliary Space: O(1)

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