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

Given a Binary Number as a string, print its 1’s and 2’s complements.

1’s complement of a binary number is another binary number obtained by toggling all bits in it, i.e., transforming the 0 bit to 1 and the 1 bit to 0.

Examples:

```1's complement of "0111" is "1000"
1's complement of "1100" is  "0011" ```

2’s complement of a binary number is 1 added to the 1’s complement of the binary number.
Examples:

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

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

For one’s complement, we simply need to flip all bits.

For 2’s complement, we first find one’s complement. We traverse the one’s complement starting from LSB (least significant bit), and look for 0. We flip all 1’s (change to 0) until we find a 0. Finally, we flip the found 0. For example, 2’s complement of “01000” is “11000” (Note that we first find one’s complement of 01000 as 10111).   If there are all 1’s (in one’s complement), we add an extra 1 in the string. For example, 2’s complement of “000” is “1000” (1’s complement of “000” is “111”).

Below is the implementation.

## C++

 `// C++ program to print 1's and 2's complement of ` `// a binary number ` `#include ` `using` `namespace` `std; ` ` `  `// Returns '0' for '1' and '1' for '0' ` `char` `flip(``char` `c) {``return` `(c == ``'0'``)? ``'1'``: ``'0'``;} ` ` `  `// Print 1's and 2's complement of binary number ` `// represented by "bin" ` `void` `printOneAndTwosComplement(string bin) ` `{ ` `    ``int` `n = bin.length(); ` `    ``int` `i; ` ` `  `    ``string ones, twos; ` `    ``ones = twos = ``""``; ` ` `  `    ``//  for ones complement flip every bit ` `    ``for` `(i = 0; i < n; i++) ` `        ``ones += flip(bin[i]); ` ` `  `    ``//  for two's complement go from right to left in ` `    ``//  ones complement and if we get 1 make, we make ` `    ``//  them 0 and keep going left when we get first ` `    ``//  0, make that 1 and go out of loop ` `    ``twos = ones; ` `    ``for` `(i = n - 1; i >= 0; i--) ` `    ``{ ` `        ``if` `(ones[i] == ``'1'``) ` `            ``twos[i] = ``'0'``; ` `        ``else` `        ``{ ` `            ``twos[i] = ``'1'``; ` `            ``break``; ` `        ``} ` `    ``} ` ` `  `    ``// If No break : all are 1  as in 111  or  11111; ` `    ``// in such case, add extra 1 at beginning ` `    ``if` `(i == -1) ` `        ``twos = ``'1'` `+ twos; ` ` `  ` `  `    ``cout << ``"1's complement: "` `<< ones << endl; ` `    ``cout << ``"2's complement: "` `<< twos << endl; ` `} ` ` `  `// Driver program ` `int` `main() ` `{ ` `    ``string bin = ``"1100"``; ` `    ``printOneAndTwosComplement(bin); ` `    ``return` `0; ` `} `

## Java

 `// Java program to print 1's and 2's complement of ` `// a binary number ` ` `  `class` `GFG  ` `{ ` ` `  `    ``// Returns '0' for '1' and '1' for '0' ` `    ``static` `char` `flip(``char` `c) ` `    ``{ ` `        ``return` `(c == ``'0'``) ? ``'1'` `: ``'0'``; ` `    ``} ` ` `  `    ``// Print 1's and 2's complement of binary number ` `    ``// represented by "bin" ` `    ``static` `void` `printOneAndTwosComplement(String bin) ` `    ``{ ` `        ``int` `n = bin.length(); ` `        ``int` `i; ` ` `  `        ``String ones = ``""``, twos = ``""``; ` `        ``ones = twos = ``""``; ` ` `  `        ``// for ones complement flip every bit ` `        ``for` `(i = ``0``; i < n; i++) ` `        ``{ ` `            ``ones += flip(bin.charAt(i)); ` `        ``} ` ` `  `        ``// for two's complement go from right to left in ` `        ``// ones complement and if we get 1 make, we make ` `        ``// them 0 and keep going left when we get first ` `        ``// 0, make that 1 and go out of loop ` `        ``twos = ones; ` `        ``for` `(i = n - ``1``; i >= ``0``; i--) ` `        ``{ ` `            ``if` `(ones.charAt(i) == ``'1'``) ` `            ``{ ` `                ``twos = twos.substring(``0``, i) + ``'0'` `+ twos.substring(i + ``1``); ` `            ``}  ` `            ``else` `            ``{ ` `                ``twos = twos.substring(``0``, i) + ``'1'` `+ twos.substring(i + ``1``); ` `                ``break``; ` `            ``} ` `        ``} ` ` `  `        ``// If No break : all are 1 as in 111 or 11111; ` `        ``// in such case, add extra 1 at beginning ` `        ``if` `(i == -``1``) ` `        ``{ ` `            ``twos = ``'1'` `+ twos; ` `        ``} ` ` `  `        ``System.out.println(``"1's complement: "` `+ ones);; ` `        ``System.out.println(``"2's complement: "` `+ twos); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``String bin = ``"1100"``; ` `        ``printOneAndTwosComplement(bin); ` `    ``} ` `} ` ` `  `// This code contributed by Rajput-Ji `

## Python3

 `# Python3 program to print 1's and 2's  ` `# complement of a binary number  ` ` `  `# Returns '0' for '1' and '1' for '0'  ` `def` `flip(c): ` `    ``return` `'1'` `if` `(c ``=``=` `'0'``) ``else` `'0'` ` `  `# Print 1's and 2's complement of  ` `# binary number represented by "bin"  ` `def` `printOneAndTwosComplement(``bin``): ` ` `  `    ``n ``=` `len``(``bin``)  ` `    ``ones ``=` `"" ` `    ``twos ``=` `"" ` `     `  `    ``# for ones complement flip every bit  ` `    ``for` `i ``in` `range``(n): ` `        ``ones ``+``=` `flip(``bin``[i])  ` ` `  `    ``# for two's complement go from right  ` `    ``# to left in ones complement and if ` `    ``# we get 1 make, we make them 0 and  ` `    ``# keep going left when we get first  ` `    ``# 0, make that 1 and go out of loop  ` `    ``ones ``=` `list``(ones.strip("")) ` `    ``twos ``=` `list``(ones) ` `    ``for` `i ``in` `range``(n ``-` `1``, ``-``1``, ``-``1``): ` `     `  `        ``if` `(ones[i] ``=``=` `'1'``): ` `            ``twos[i] ``=` `'0'` `        ``else``:          ` `            ``twos[i] ``=` `'1'` `            ``break` ` `  `    ``i ``-``=` `1`     `    ``# If No break : all are 1 as in 111 or 11111  ` `    ``# in such case, add extra 1 at beginning  ` `    ``if` `(i ``=``=` `-``1``): ` `        ``twos.insert(``0``, ``'1'``)  ` ` `  `    ``print``(``"1's complement: "``, ``*``ones, sep ``=` `"") ` `    ``print``(``"2's complement: "``, ``*``twos, sep ``=` `"") ` `     `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``bin` `=` `"1100"` `    ``printOneAndTwosComplement(``bin``.strip("")) ` `     `  `# This code is contributed  ` `# by SHUBHAMSINGH10 `

## C#

 `// C# program to print 1's and 2's complement of ` `// a binary number ` `using` `System; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``// Returns '0' for '1' and '1' for '0' ` `    ``static` `char` `flip(``char` `c) ` `    ``{ ` `        ``return` `(c == ``'0'``) ? ``'1'` `: ``'0'``; ` `    ``} ` ` `  `    ``// Print 1's and 2's complement of binary number ` `    ``// represented by "bin" ` `    ``static` `void` `printOneAndTwosComplement(String bin) ` `    ``{ ` `        ``int` `n = bin.Length; ` `        ``int` `i; ` ` `  `        ``String ones = ``""``, twos = ``""``; ` `        ``ones = twos = ``""``; ` ` `  `        ``// for ones complement flip every bit ` `        ``for` `(i = 0; i < n; i++) ` `        ``{ ` `            ``ones += flip(bin[i]); ` `        ``} ` ` `  `        ``// for two's complement go from right to left in ` `        ``// ones complement and if we get 1 make, we make ` `        ``// them 0 and keep going left when we get first ` `        ``// 0, make that 1 and go out of loop ` `        ``twos = ones; ` `        ``for` `(i = n - 1; i >= 0; i--) ` `        ``{ ` `            ``if` `(ones[i] == ``'1'``) ` `            ``{ ` `                ``twos = twos.Substring(0, i) + ``'0'` `+  ` `                ``twos.Substring(i + 1,twos.Length-(i+1)); ` `            ``}  ` `            ``else` `            ``{ ` `                ``twos = twos.Substring(0, i) + ``'1'` `+  ` `                ``twos.Substring(i + 1,twos.Length-(i+1)); ` `                ``break``; ` `            ``} ` `        ``} ` ` `  `        ``// If No break : all are 1 as in 111 or 11111; ` `        ``// in such case, add extra 1 at beginning ` `        ``if` `(i == -1) ` `        ``{ ` `            ``twos = ``'1'` `+ twos; ` `        ``} ` ` `  `        ``Console.WriteLine(``"1's complement: "` `+ ones);; ` `        ``Console.WriteLine(``"2's complement: "` `+ twos); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``String bin = ``"1100"``; ` `        ``printOneAndTwosComplement(bin); ` `    ``} ` `} ` ` `  `// This code has been contributed by 29AjayKumar `

Output:

```1's complement: 0011
2's complement: 0100```

Thanks to Utkarsh Trivedi for above solution.

As a side note, signed numbers generally use 2’s complement representation. Positive values are stored as it is and negative values are stored in their 2’s complement form. One extra bit is required to indicate whether number is positive or negative. For example char is 8 bits in C. If 2’s complement representation is used for char, then 127 is stored as it is, i.e., 01111111 where first 0 indicates positive. But -127 is stored as 10000001.

Related Post :

Efficient method for 2’s complement of a binary string