Count of N-bit binary numbers without leading zeros
Given an integer N, the task is to find the count of N-bit binary numbers without leading zeros.
Examples:
Input: N = 2
Output: 2
10 and 11 are the only possible binary numbers.
Input: N = 4
Output: 8
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 <bits/stdc++.h> 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; } |
chevron_right
filter_none
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 |
chevron_right
filter_none
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 |
chevron_right
filter_none
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 |
chevron_right
filter_none
Output:
8
Recommended Posts:
- Count numbers having N 0's and and M 1's with no leading zeros
- Comparing leading zeros in binary representations of two numbers
- All possible numbers of N digits and base B without leading zeros
- Number of leading zeros in binary representation of a given number
- Count unique numbers that can be generated from N by adding one and removing trailing zeros
- Count number of trailing zeros in Binary representation of a number using Bitset
- Count numbers have all 1s together in binary representation
- Count of Binary Digit numbers smaller than N
- Count number of trailing zeros in (1^1)*(2^2)*(3^3)*(4^4)*..
- Count number of trailing zeros in product of array
- Minimum count of Full Binary Trees such that the count of leaves is N
- Count numbers < = N whose difference with the count of primes upto them is > = K
- Count numbers which can be constructed using two numbers
- Count numbers which are divisible by all the numbers from 2 to 10
- Count numbers that don't contain 3
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.
- Find next greater element with no consecutive 1 in it's binary representation
- Number of K length subsequences with minimum sum
- Printing the Triangle Pattern using last term N
- Sum of values of all possible non-empty subsets of the given array
- Minimum steps required to reduce all the elements of the array to zero