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

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  • Difficulty Level : Easy
  • Last Updated : 05 Jul, 2022
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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.In the 1’s complement format , the positive numbers remain unchanged . The negative numbers are obtained by taking the 1’s complement of positive counterparts.

for example +9 will be represented as 00001001 in eight-bit notation and -9 will be represented as 11110110, which is the 1’s complement of 00001001.

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. In the 2’s complement representation of binary numbers, the MSB represents the sign with a ‘0’ used for plus sign and a  ‘1’ used for a minus sign. the remaining bits are used for representing magnitude. positive magnitudes are represented in the same way as in the case of sign-bit or 1’s complement representation.  Negative magnitudes are represented by the 2’s complement of their positive counterparts.

Examples: 

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

Another trick to finding two’s complement:

Step 1:  Start from the Least Significant Bit and traverse left until you find a 1.  Until you find 1, the bits stay the same

Step 2: Once you have found 1, let the 1 as it is, and now

Step 3: Flip all the bits left into the 1.

Illustration

Suppose we need to find 2s Complement of 100100

Step 1: Traverse and let the bit stay the same until you find 1. Here x is not known yet. Answer = xxxx00 –

Step 2: You found 1. Let it stay the same. Answer = xxx100

Step 3: Flip all the bits left into the 1. Answer = 011100.

Hence, the 2s complement of 100100 is 011100.

Recommended Practice

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 <bits/stdc++.h>
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


Javascript




<script>
 
// Javascript program to print 1's and 2's complement of
// a binary number
 
// Returns '0' for '1' and '1' for '0'
function flip (c) {return (c == '0')? '1': '0';}
 
// Print 1's and 2's complement of binary number
// represented by "bin"
function printOneAndTwosComplement(bin)
{
    var n = bin.length;
    var i;
 
    var 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;
    twos = twos.split('')
    for (i = n - 1; i >= 0; i--)
    {
        if (ones[i] == '1')
            twos[i] = '0';
        else
        {
            twos[i] = '1';
            break;
        }
    }
    twos = twos.join('')
    // 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;
 
 
    document.write( "1's complement: " + ones + "<br>");
    document.write( "2's complement: " + twos + "<br>");
}
 
// Driver program
var bin = "1100";
printOneAndTwosComplement(bin);
 
</script>


Output: 

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

Time Complexity: O(n)

Auxiliary Space: O(1)

Thanks to Utkarsh Trivedi for the 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 the 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
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
References: 
http://qa.geeksforgeeks.org/6439/write-program-calculate-ones-and-twos-complement-of-number 
http://geeksquiz.com/whats-difference-between-1s-complement-and-2s-complement/
 


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