# Add two unsigned numbers using bits in C++.

CServer Side ProgrammingProgramming

An unsigned number represented as a stream of bits is written in binary form.

The binary form of 54 is 110110.

Rules for bit addition is −

• 0+0 = 0
• 1+0 = 1
• 0+1 = 1
• 1+1 = 0 with carry = 1

Lets take an example to add two numbers,

Input: a = 21 (10101) , b = 27 (11011)
Output: 48 (110000)

Explanation − 10101 + 11011 = 110000. We will add bits starting the least significant bit. And then propagating to the next bit.

## Example

#include <bits/stdc++.h>
#define M 32
using namespace std;
int binAdd (bitset < M > atemp, bitset < M > btemp){
bitset < M > ctemp;
for (int i = 0; i < M; i++)
ctemp[i] = 0;
int carry = 0;
for (int i = 0; i < M; i++) {
if (atemp[i] + btemp[i] == 0){
if (carry == 0)
ctemp[i] = 0;
Else {
ctemp[i] = 1;
carry = 0;
}
}
else if (atemp[i] + btemp[i] == 1){
if (carry == 0)
ctemp[i] = 1;
else{
ctemp[i] = 0;
}
}
else{
if (carry == 0){
ctemp[i] = 0;
carry = 1;
}
else{
ctemp[i] = 1;
}
}
}
return ctemp.to_ulong ();
}
int main () {
int a = 678, b = 436;
cout << "The sum of " << a << " and " << b << " is ";
bitset < M > num1 (a);
bitset < M > num2 (b);
cout << binAdd (num1, num2) << endl;
}

## Output

The sum of 678 and 436 is 1114