# Count of total bits toggled/flipped in binary representation of 0 to N

Given an integer N, the task is to find the total number of bits toggled to obtain all numbers from 0 to N sequentially.

Examples:

Input: N = 5
Output:
Explanation:
Let’s represent numbers from 0 to 5 in binary:
000 -> 001 : 1 bit toggled
001 -> 010 : 2 bits toggled
010 -> 011 : 1 bit toggled
011 -> 100 : 3 bits toggled
100 -> 101 : 1 bit toggled
Hence, 8 bits toggled

Input: N = 1
Output: 1

Approach:
Follow the steps below to solve the problems:

• The following observations need to be made to solve the problem:

The rightmost bit toggles every time.
(000) -> (001) -> (010) -> (011
So, the contribution of this bit to the count will be N
The next bit toggles after every 2 numbers.
(000) -> (001) -> (010) -> (011) -> (100)
Hence, the contribution of this bit to the count will be N/2.

• Thus, we can conclude that the i th least significant bit will contribute N/(2 i) to the count of toggles.
• Hence, the sum of N/(2i) where i is in the range [0, log2N], gives the required answer.
• Hence, initialize a variable ans. Add N to ans and update N to N/2. Repeat this process until N becomes 0, to get the final result.

Below is the implementation of the above approach:

## C++

 `// C++ program to count ` `// the number of toggles ` `// required to generate ` `// all numbers from 0 to N `   `#include ` `using` `namespace` `std; `   `typedef` `long` `long` `int` `ll; `   `// Function to count and print ` `// the required number of ` `// toggles ` `void` `solve(ll N) ` `{ ` `    ``// Store the count ` `    ``// of toggles ` `    ``ll ans = 0; `   `    ``while` `(N != 0) { `   `        ``// Add the contribution ` `        ``// of the current LSB ` `        ``ans += N; `   `        ``// Update N ` `        ``N /= 2; ` `    ``} ` `    ``// Print the result ` `    ``cout << ans << endl; ` `} ` `// Driver code ` `int` `main() ` `{ ` `    ``ll N = 5; ` `    ``solve(N); ` `    ``return` `0; ` `} `

## Java

 `// Java program to count the ` `// number of toggles required ` `// to generate all numbers ` `// from 0 to N ` `class` `GFG{ `   `// Function to count and print ` `// the required number of ` `// toggles ` `static` `void` `solve(``int` `N) ` `{ ` `    `  `    ``// Store the count ` `    ``// of toggles ` `    ``int` `ans = ``0``; `   `    ``while` `(N != ``0``) ` `    ``{ ` `        `  `        ``// Add the contribution ` `        ``// of the current LSB ` `        ``ans += N; `   `        ``// Update N ` `        ``N /= ``2``; ` `    ``} ` `    `  `    ``// Print the result ` `    ``System.out.println(ans); ` `} `   `// Driver code ` `public` `static` `void` `main(String []args) ` `{ ` `    ``int` `N = ``5``; ` `    `  `    ``solve(N); ` `} ` `} `   `// This code is contributed by Ritik Bansal `

## Python3

 `# Python3 program to count ` `# the number of toggles ` `# required to generate ` `# all numbers from 0 to N `   `# Function to count and pr ` `# the required number of ` `# toggles ` `def` `solve(N): ` `    `  `    ``# Store the count ` `    ``# of toggles ` `    ``ans ``=` `0`   `    ``while` `(N !``=` `0``): `   `        ``# Add the contribution ` `        ``# of the current LSB ` `        ``ans ``+``=` `N `   `        ``# Update N ` `        ``N ``/``/``=` `2` `    `  `    ``# Print the result ` `    ``print``(ans) `   `# Driver code ` `N ``=` `5`   `solve(N) `   `# This code is contributed by code_hunt`

## C#

 `// C# program to count the ` `// number of toggles required` `// to generate all numbers ` `// from 0 to N` `using` `System;`   `class` `GFG{`   `// Function to count and print` `// the required number of` `// toggles` `static` `void` `solve(``int` `N)` `{` `    `  `    ``// Store the count` `    ``// of toggles` `    ``int` `ans = 0;`   `    ``while` `(N != 0)` `    ``{` `        `  `        ``// Add the contribution` `        ``// of the current LSB` `        ``ans += N;`   `        ``// Update N` `        ``N /= 2;` `    ``}` `    `  `    ``// Print the result` `    ``Console.Write(ans);` `}`   `// Driver code` `public` `static` `void` `Main(``string` `[]args)` `{` `    ``int` `N = 5;` `    `  `    ``solve(N);` `}` `}`   `// This code is contributed by rock_cool`

## Javascript

 ``

Output:

`8`

Time Complexity: O(log N)
Auxiliary Space: O(1)

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