# Count unset bits of a number

Given a number n, count unset bits after MSB (Most Significant Bit).**Examples :**

Input : 17 Output : 3 Binary of 17 is 10001 so unset bit is 3 Input : 7 Output : 0

A **Simple Solution **is to traverse through all bits and count unset bits.

## C++

`// C++ program to count unset bits in an integer` `#include <iostream>` `using` `namespace` `std;` `int` `countunsetbits(` `int` `n)` `{` ` ` `int` `count = 0; ` ` ` ` ` `// x holds one set digit at a time` ` ` `// starting from LSB to MSB of n.` ` ` `for` `(` `int` `x = 1; x <= n; x = x<<1) ` ` ` `if` `((x & n) == 0)` ` ` `count++; ` ` ` `return` `count; ` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 17;` ` ` `cout << countunsetbits(n); ` ` ` `return` `0;` `}` |

## Java

`// JAVA Code to Count unset bits in a number` `class` `GFG {` ` ` `public` `static` `int` `countunsetbits(` `int` `n)` ` ` `{` ` ` `int` `count = ` `0` `; ` ` ` ` ` `// x holds one set digit at a time` ` ` `// starting from LSB to MSB of n.` ` ` `for` `(` `int` `x = ` `1` `; x <= n; x = x<<` `1` `) ` ` ` `if` `((x & n) == ` `0` `)` ` ` `count++; ` ` ` ` ` `return` `count; ` ` ` `}` ` ` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{` ` ` `int` `n = ` `17` `;` ` ` `System.out.println(countunsetbits(n)); ` ` ` `}` `}` `// This code is contributed by Arnav Kr. Mandal.` |

## Python3

`# Python 3 program to count unset ` `# bits in an integer` `def` `countunsetbits(n):` ` ` `count ` `=` `0` ` ` ` ` `# x holds one set digit at a time` ` ` `# starting from LSB to MSB of n.` ` ` `x ` `=` `1` ` ` `while` `(x < n ` `+` `1` `):` ` ` `if` `((x & n) ` `=` `=` `0` `):` ` ` `count ` `+` `=` `1` ` ` `x ` `=` `x << ` `1` ` ` `return` `count ` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `n ` `=` `17` ` ` `print` `(countunsetbits(n)) ` ` ` `# This code is contributed by` `# Shashank_Sharma` |

## C#

`// C# Code to Count unset ` `// bits in a number` `using` `System;` `class` `GFG {` ` ` `// Function to count unset bits` ` ` `public` `static` `int` `countunsetbits(` `int` `n)` ` ` `{` ` ` `int` `count = 0; ` ` ` ` ` `// x holds one set digit at a time` ` ` `// starting from LSB to MSB of n.` ` ` `for` `(` `int` `x = 1; x <= n; x = x << 1) ` ` ` `if` `((x & n) == 0)` ` ` `count++; ` ` ` ` ` `return` `count; ` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main() ` ` ` `{` ` ` `int` `n = 17;` ` ` `Console.Write(countunsetbits(n)); ` ` ` `}` `}` `// This code is contributed by Nitin Mittal.` |

## PHP

`<?php` `// PHp program to count` `// unset bits in an integer` `function` `countunsetbits(` `$n` `)` `{` ` ` `$count` `= 0; ` ` ` ` ` `// x holds one set digit` ` ` `// at a time starting ` ` ` `// from LSB to MSB of n.` ` ` `for` `(` `$x` `= 1; ` `$x` `<= ` `$n` `; ` ` ` `$x` `= ` `$x` `<< 1) ` ` ` `if` `((` `$x` `& ` `$n` `) == 0)` ` ` `$count` `++; ` ` ` `return` `$count` `; ` `}` `// Driver code` `$n` `= 17;` `echo` `countunsetbits(` `$n` `); ` `// This code is contributed` `// by nitin mittal.` `?>` |

## Javascript

`<script>` `// Javascript program to count unset bits in an integer` `function` `countunsetbits(n)` `{` ` ` `var` `count = 0; ` ` ` ` ` `// x holds one set digit at a time` ` ` `// starting from LSB to MSB of n.` ` ` `for` `(` `var` `x = 1; x <= n; x = x<<1) ` ` ` `if` `((x & n) == 0)` ` ` `count++; ` ` ` `return` `count; ` `}` `// Driver code` `var` `n = 17;` `document.write(countunsetbits(n)); ` `</script>` |

**Output :**

3

Above solution complexity is** log(n)**.**Efficient Solutions : **

The idea is to toggle bits in O(1) time. Then apply any of the methods discussed in count set bits article.

In GCC, we can directly count set bits using __builtin_popcount(). First toggle the bits and then apply above function __builtin_popcount().

## C++

`// An optimized C++ program to count unset bits` `// in an integer.` `#include <iostream>` `using` `namespace` `std;` `int` `countUnsetBits(` `int` `n)` `{` ` ` `int` `x = n;` ` ` ` ` `// Make all bits set MSB ` ` ` `// (including MSB)` ` ` ` ` `// This makes sure two bits` ` ` `// (From MSB and including MSB)` ` ` `// are set` ` ` `n |= n >> 1;` ` ` `// This makes sure 4 bits` ` ` `// (From MSB and including MSB)` ` ` `// are set` ` ` `n |= n >> 2;` ` ` `n |= n >> 4;` ` ` `n |= n >> 8;` ` ` `n |= n >> 16;` ` ` `// Count set bits in toggled number` ` ` `return` `__builtin_popcount(x ^ n);` `}` `// Driver code` `int` `main()` `{` ` ` `int` `n = 17;` ` ` `cout << countUnsetBits(n);` ` ` `return` `0;` `}` |

## Java

`// An optimized Java program to count unset bits ` `// in an integer. ` `class` `GFG ` `{` `static` `int` `countUnsetBits(` `int` `n) ` `{ ` ` ` `int` `x = n; ` ` ` `// Make all bits set MSB ` ` ` `// (including MSB) ` ` ` ` ` `// This makes sure two bits ` ` ` `// (From MSB and including MSB) ` ` ` `// are set ` ` ` `n |= n >> ` `1` `; ` ` ` `// This makes sure 4 bits ` ` ` `// (From MSB and including MSB) ` ` ` `// are set ` ` ` `n |= n >> ` `2` `; ` ` ` `n |= n >> ` `4` `; ` ` ` `n |= n >> ` `8` `; ` ` ` `n |= n >> ` `16` `; ` ` ` `// Count set bits in toggled number ` ` ` `return` `Integer.bitCount(x^ n); ` `} ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{` ` ` `int` `n = ` `17` `; ` ` ` `System.out.println(countUnsetBits(n));` `}` `}` `/* This code contributed by PrinciRaj1992 */` |

## Python3

`# An optimized Python program to count ` `# unset bits in an integer.` `import` `math` `def` `countUnsetBits(n):` ` ` `x ` `=` `n` ` ` `# Make all bits set MSB(including MSB)` ` ` `# This makes sure two bits(From MSB ` ` ` `# and including MSB) are set` ` ` `n |` `=` `n >> ` `1` ` ` `# This makes sure 4 bits(From MSB and ` ` ` `# including MSB) are set` ` ` `n |` `=` `n >> ` `2` ` ` `n |` `=` `n >> ` `4` ` ` `n |` `=` `n >> ` `8` ` ` `n |` `=` `n >> ` `16` ` ` `t ` `=` `math.log(x ^ n, ` `2` `)` ` ` `# Count set bits in toggled number` ` ` `return` `math.floor(t)` `# Driver code` `n ` `=` `17` `print` `(countUnsetBits(n))` `# This code is contributed 29AjayKumar` |

## C#

`// An optimized C# program to count unset bits ` `// in an integer.` `using` `System;` `class` `GFG ` `{ ` `static` `int` `countUnsetBits(` `int` `n) ` `{ ` ` ` `int` `x = n; ` ` ` `// Make all bits set MSB ` ` ` `// (including MSB) ` ` ` ` ` `// This makes sure two bits ` ` ` `// (From MSB and including MSB) ` ` ` `// are set ` ` ` `n |= n >> 1; ` ` ` `// This makes sure 4 bits ` ` ` `// (From MSB and including MSB) ` ` ` `// are set ` ` ` `n |= n >> 2; ` ` ` `n |= n >> 4; ` ` ` `n |= n >> 8; ` ` ` `n |= n >> 16; ` ` ` `// Count set bits in toggled number ` ` ` `return` `BitCount(x^ n); ` `} ` `static` `int` `BitCount(` `long` `x)` `{` ` ` `// To store the count` ` ` `// of set bits` ` ` `int` `setBits = 0;` ` ` `while` `(x != 0) {` ` ` `x = x & (x - 1);` ` ` `setBits++;` ` ` `}` ` ` `return` `setBits;` `}` `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ` `int` `n = 17; ` ` ` `Console.WriteLine(countUnsetBits(n)); ` `} ` `} ` `// This code contributed by Rajput-Ji` |

## PHP

`<?php` `// An optimized PHP program ` `// to count unset bits in ` `// an integer.` `function` `countUnsetBits(` `$n` `)` `{` ` ` `$x` `= ` `$n` `;` ` ` `// Make all bits set ` ` ` `// MSB(including MSB)` ` ` `// This makes sure two ` ` ` `// bits(From MSB and ` ` ` `// including MSB) are set` ` ` `$n` `|= ` `$n` `>> 1;` ` ` `// This makes sure 4 ` ` ` `// bits(From MSB and ` ` ` `// including MSB) are set` ` ` `$n` `|= ` `$n` `>> 2;` ` ` `$n` `|= ` `$n` `>> 4;` ` ` `$n` `|= ` `$n` `>> 8;` ` ` `$n` `|= ` `$n` `>> 16;` ` ` `$t` `= log(` `$x` `^ ` `$n` `,2);` ` ` ` ` `// Count set bits ` ` ` `// in toggled number` ` ` `return` `floor` `(` `$t` `);` `}` `// Driver code` `$n` `= 17;` `echo` `countUnsetBits(` `$n` `);` `// This code is contributed` `// by ajit ` `?>` |

## Javascript

`<script>` `// JavaScript program to count unset bits` `// in an integer.` `function` `countUnsetBits(n)` `{` ` ` `let x = n;` ` ` ` ` `// Make all bits set MSB` ` ` `// (including MSB)` ` ` ` ` `// This makes sure two bits` ` ` `// (From MSB and including MSB)` ` ` `// are set` ` ` `n |= n >> 1;` ` ` ` ` `// This makes sure 4 bits` ` ` `// (From MSB and including MSB)` ` ` `// are set` ` ` `n |= n >> 2;` ` ` ` ` `n |= n >> 4;` ` ` `n |= n >> 8;` ` ` `n |= n >> 16;` ` ` ` ` `// Count set bits in toggled number` ` ` `return` `BitCount(x^ n);` `}` `function` `BitCount(x)` `{` ` ` ` ` `// To store the count` ` ` `// of set bits` ` ` `let setBits = 0;` ` ` `while` `(x != 0) {` ` ` `x = x & (x - 1);` ` ` `setBits++;` ` ` `}` ` ` ` ` `return` `setBits;` `}` `// Driver Code` ` ` `let n = 17;` ` ` `document.write(countUnsetBits(n));` `// This code is contributed by susmitakundugoaldanga.` `</script>` |

**Output :**

3

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