# Efficient method for 2’s complement of a binary string

Given a Binary Number as string, print its 2’s complements.**2’s complement **of a binary number is 1 added to the 1’s complement of the binary number. Note that 1’s complement is simply flip of given binary number.

**Examples:**

2's complement of "0111" is "1001" 2's complement of "1100" is "0100"

## We strongly recommend that you click here and practice it, before moving on to the solution.

We have discussed 1’s and 2’s complements in below post.

1’s and 2’s complement of a Binary Number.

The method discussed in above post traverses binary string twice to find 2’s complement, first finds 1’s complement, then finds 2’s complement using 1’s complement

In this post an efficient method for 2’s complement is discussed that **traverses string only once**. We traverse the string from last till the single 1 is not traversed and after that flip all values of string i.e. 0 to 1 and 1 to 0.

**Note: **Here to handle the corner case i.e. if 1 doesn’t exist in the string then just append 1 in the starting of string.

**Illustration :**

Input:str = "1000100"Output:0111100 Explanation: Starts traversing the string from last, we got first '1' at index 4 then just flip the bits of 0 to 3 indexes to make the 2's complement.Input:str = "0000"Output:10000 Explanation: As there is no 1 in the string so just append '1' at starting.

**Implementation:**

## C++

`// An efficient C++ program to find 2's complement` `#include<bits/stdc++.h>` `using` `namespace` `std;` `// Function to find two's complement` `string findTwoscomplement(string str)` `{` ` ` `int` `n = str.length();` ` ` `// Traverse the string to get first '1' from` ` ` `// the last of string` ` ` `int` `i;` ` ` `for` `(i = n-1 ; i >= 0 ; i--)` ` ` `if` `(str[i] == ` `'1'` `)` ` ` `break` `;` ` ` `// If there exists no '1' concatenate 1 at the` ` ` `// starting of string` ` ` `if` `(i == -1)` ` ` `return` `'1'` `+ str;` ` ` `// Continue traversal after the position of` ` ` `// first '1'` ` ` `for` `(` `int` `k = i-1 ; k >= 0; k--)` ` ` `{` ` ` `//Just flip the values` ` ` `if` `(str[k] == ` `'1'` `)` ` ` `str[k] = ` `'0'` `;` ` ` `else` ` ` `str[k] = ` `'1'` `;` ` ` `}` ` ` `// return the modified string` ` ` `return` `str;` `}` `// Driver code` `int` `main()` `{` ` ` `string str = ` `"00000101"` `;` ` ` `cout << findTwoscomplement(str);` ` ` `return` `0;` `} ` |

## Java

`// An efficient Java program to find 2's complement` `class` `Test` `{` ` ` `// Method to find two's complement` ` ` `static` `String findTwoscomplement(StringBuffer str)` ` ` `{` ` ` `int` `n = str.length();` ` ` ` ` `// Traverse the string to get first '1' from` ` ` `// the last of string` ` ` `int` `i;` ` ` `for` `(i = n-` `1` `; i >= ` `0` `; i--)` ` ` `if` `(str.charAt(i) == ` `'1'` `)` ` ` `break` `;` ` ` ` ` `// If there exists no '1' concat 1 at the` ` ` `// starting of string` ` ` `if` `(i == -` `1` `)` ` ` `return` `"1"` `+ str;` ` ` ` ` `// Continue traversal after the position of` ` ` `// first '1'` ` ` `for` `(` `int` `k = i-` `1` `; k >= ` `0` `; k--)` ` ` `{` ` ` `//Just flip the values` ` ` `if` `(str.charAt(k) == ` `'1'` `)` ` ` `str.replace(k, k+` `1` `, ` `"0"` `);` ` ` `else` ` ` `str.replace(k, k+` `1` `, ` `"1"` `);` ` ` `}` ` ` ` ` `// return the modified string` ` ` `return` `str.toString();` ` ` `}` ` ` ` ` `// Driver method` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `StringBuffer str = ` `new` `StringBuffer(` `"00000101"` `);` ` ` `System.out.println(findTwoscomplement(str));` ` ` `}` `}` |

## Python3

`# An efficient Python 3 program to` `# find 2's complement` `# Function to find two's complement` `def` `findTwoscomplement(` `str` `):` ` ` `n ` `=` `len` `(` `str` `)` ` ` `# Traverse the string to get first` ` ` `# '1' from the last of string` ` ` `i ` `=` `n ` `-` `1` ` ` `while` `(i >` `=` `0` `):` ` ` `if` `(` `str` `[i] ` `=` `=` `'1'` `):` ` ` `break` ` ` `i ` `-` `=` `1` ` ` `# If there exists no '1' concatenate 1` ` ` `# at the starting of string` ` ` `if` `(i ` `=` `=` `-` `1` `):` ` ` `return` `'1'` `+` `str` ` ` `# Continue traversal after the` ` ` `# position of first '1'` ` ` `k ` `=` `i ` `-` `1` ` ` `while` `(k >` `=` `0` `):` ` ` ` ` `# Just flip the values` ` ` `if` `(` `str` `[k] ` `=` `=` `'1'` `):` ` ` `str` `=` `list` `(` `str` `)` ` ` `str` `[k] ` `=` `'0'` ` ` `str` `=` `''.join(` `str` `)` ` ` `else` `:` ` ` `str` `=` `list` `(` `str` `)` ` ` `str` `[k] ` `=` `'1'` ` ` `str` `=` `''.join(` `str` `)` ` ` `k ` `-` `=` `1` ` ` `# return the modified string` ` ` `return` `str` `# Driver code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` `str` `=` `"00000101"` ` ` `print` `(findTwoscomplement(` `str` `))` `# This code is contributed by` `# Sanjit_Prasad` |

## C#

`// An efficient c# program to find 2's complement` `using` `System;` `using` `System.Text;` `class` `GFG` `{` `// Method to find two's complement` `public` `static` `string` `findTwoscomplement(StringBuilder str)` `{` ` ` `int` `n = str.Length;` ` ` `// Traverse the string to get` ` ` `// first '1' from the last of string` ` ` `int` `i;` ` ` `for` `(i = n - 1 ; i >= 0 ; i--)` ` ` `{` ` ` `if` `(str[i] == ` `'1'` `)` ` ` `{` ` ` `break` `;` ` ` `}` ` ` `}` ` ` `// If there exists no '1' concat 1` ` ` `// at the starting of string` ` ` `if` `(i == -1)` ` ` `{` ` ` `return` `"1"` `+ str;` ` ` `}` ` ` `// Continue traversal after the` ` ` `// position of first '1'` ` ` `for` `(` `int` `k = i - 1 ; k >= 0; k--)` ` ` `{` ` ` `// Just flip the values` ` ` `if` `(str[k] == ` `'1'` `)` ` ` `{` ` ` `str.Remove(k, k + 1 - k).Insert(k, ` `"0"` `);` ` ` `}` ` ` `else` ` ` `{` ` ` `str.Remove(k, k + 1 - k).Insert(k, ` `"1"` `);` ` ` `}` ` ` `}` ` ` `// return the modified string` ` ` `return` `str.ToString();` `}` `// Driver Code` `public` `static` `void` `Main(` `string` `[] args)` `{` ` ` `StringBuilder str = ` `new` `StringBuilder(` `"00000101"` `);` ` ` `Console.WriteLine(findTwoscomplement(str));` `}` `}` `// This code is contributed by Shrikant13` |

## PHP

`<?php` `// An efficient PHP program to find 2's` `// complement` `// Function to find two's complement` `function` `findTwoscomplement(` `$str` `)` `{` ` ` `$n` `= ` `strlen` `(` `$str` `);` ` ` `// Traverse the string to get first` ` ` `// '1' from the last of string` ` ` `$i` `;` ` ` `for` `(` `$i` `= ` `$n` `-1 ; ` `$i` `>= 0 ; ` `$i` `--)` ` ` `if` `(` `$str` `[` `$i` `] == ` `'1'` `)` ` ` `break` `;` ` ` `// If there exists no '1' concatenate` ` ` `// 1 at the starting of string` ` ` `if` `(` `$i` `== -1)` ` ` `return` `'1'` `+ ` `$str` `;` ` ` `// Continue traversal after the` ` ` `// position of first '1'` ` ` `for` `(` `$k` `= ` `$i` `-1 ; ` `$k` `>= 0; ` `$k` `--)` ` ` `{` ` ` `// Just flip the values` ` ` `if` `(` `$str` `[` `$k` `] == ` `'1'` `)` ` ` `$str` `[` `$k` `] = ` `'0'` `;` ` ` `else` ` ` `$str` `[` `$k` `] = ` `'1'` `;` ` ` `}` ` ` `// return the modified string` ` ` `return` `$str` `;;` `}` `// Driver code` `$str` `= ` `"00000101"` `;` `echo` `findTwoscomplement(` `$str` `);` `// This code is contributed by jit.` `?>` |

## Javascript

`<script>` `// An efficient javascript program to find 2's complement` ` ` `// Method to find two's complement` ` ` `function` `findTwoscomplement( str) {` ` ` `var` `n = str.length;` ` ` `// Traverse the string to get first '1' from` ` ` `// the last of string` ` ` `var` `i;` ` ` `for` `(i = n - 1; i >= 0; i--)` ` ` `if` `(str.charAt(i) == ` `'1'` `)` ` ` `break` `;` ` ` `// If there exists no '1' concat 1 at the` ` ` `// starting of string` ` ` `if` `(i == -1)` ` ` `return` `"1"` `+ str;` ` ` `// Continue traversal after the position of` ` ` `// first '1'` ` ` `for` `(k = i - 1; k >= 0; k--) {` ` ` `// Just flip the values` ` ` `if` `(str.charAt(k) == ` `'1'` `)` ` ` `str = str.substring(0,k)+` `"0"` `+str.substring(k+1, str.length);` ` ` `else` ` ` `str = str.substring(0,k)+` `"1"` `+str.substring(k+1, str.length);` ` ` `}` ` ` `// return the modified string` ` ` `return` `str.toString();` ` ` `}` ` ` `// Driver method` ` ` ` ` `var` `str = ` `"00000101"` `;` ` ` `document.write(findTwoscomplement(str));` `// This code contributed by umadevi9616` `</script>` |

**Output**

11111011

**Time complexity** **: O(n) ****Auxiliary Space : O(1)**

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