Finding Twos complement,

Question

Here is the code to compute: anyone, with help to convert a signed integer to its binary equivalent (8 bits) (in 2's complement) and vice versa. The program should be able t0 first read in either a signed integer or a binary number (always in 2's complement) provided by the user

For example, when I input 00110101 to convert to signed decimal, I will get 203 . But the correct answer is 53 .

#include <iostream>
#include <string>

using namespace std;

string decimalToBinary(int);
string findTwosComplement(string);

string decimalToBinary(int n) {
    if (n < 0)
        n = 256 + n;
    string res = "";
    while (n > 0)
    {
        res = string(1, (char)(n % 2 + 48)) + res;
        n = n / 2;
    }
    return res;
}

string decimalToBinary(int n) {
    if (n < 0)
        n = 256 + n;
    string res = "";
    while (n > 0)
    {
        res = string(1, (char)(n % 2 + 48)) + res;
        n = n / 2;
    }
    return res;
}

string findTwosComplement(string s)
{
        int num = s.length();

    int i;
    for (i = num - 1; i >= 0; i--)
        if (s[i] == '1')
            break;
    if (i == -1)
        return '1' + s;
    for (int j = i - 1; j >= 0; j--)
    {
        if (s[j] == '1')
            s[j] = '0';
        else
            s[j] = '1';
    }
    return s;
}

Answer 1

I am assuming you want this for didactic purpose, other wise you just do (signed char) n .

The two complements is -2<<(n-1) + sum(2<<k for 0 <= k < n-1) so for 8-bit you have the usual binary representation for the numbers 0 <= N < 128 the difference is that the most significant bit is not adding 128, but subtracting 128. This is why it can represent numbers -128 <= N < 128 . Important thing is that you can increase the width of the number by replicating the signal digit. C++ numbers are already 2-complements 32-bit numbers, so for the numbers in the valid range the 24 most significant bits are either all '0' or all '1', so you can just slice the bits there.

#include <iostream>
#include <string>

using namespace std;

string decimalToBinary(int n) {
    // C++ integers are already in 2-complements so you only have to 
    // extract the bits.
    if((n < -128) || (n >= 128)){
      std::cerr << "The number "<< n << " does not fit into a 8-bit 2-complement representation" << std::endl;
    }
    string res = "";
    for(int i = 0; i < 8; ++i){
      res = string(1, (char)(((n >> i) & 1) + '0')) + res;
    }
    return res;
}

int binaryToDecimal(string s) {
  // The most significant bit is the signal
  int result = -((int)(s[0] - '0'));

  for(int i = 1; i < s.size(); ++i){
    result = 2*result + ((int)(s[i] - '0'));
  }
  return result;
}

int main(){
  int input;
  while(cin){
    cout << "> ";
    cin >> input;
    string binary = decimalToBinary(input);
    int output = binaryToDecimal(binary);
    cout << input << " -> " << binary << " -> " << output << endl;
  }
}