Adding two number's without +

Write code for adding two n-bit and assume that your code will run on a machine which doesn’t have ADD instruction which means that you can’t use the + operator.


Approach : Make a 1 bit adder and then cascade it to work for n bits i.e. assuming that we are adding 32 bit numbers then it will work for 32 bits.

To figure out the equation for a 1 bit adder we will write the truth table for a 1-bit adder.

A B Sum Carry

0 0 0 0

0 1 1 0

1 1 0 1

1 0 1 0

So now if you look the SUM column is A’B + AB’ which is (A XOR B)

Carry is (A AND B)

Code for the above approach

int
Nbitadder (int no1, int no2)

{

Int carry = 0;

Int totalSum = 0;

For (i=0; I < sizeof(int) ; i++)

{

// Shift the bit to get it to the first position for both numbers

Bit1no1 = no1 >> i;

Bit1no2 = no2 >> i;

// Mask out all the other bits except the first bit.

Bit1no1 = bit1no1 & 0x00000001;

Bit1no2 = bit2no2 & 0x00000001;

If ( carry == 0)

{

Sum = bit1no1 XOR bit1no2; // Add the two bits

Carry = bit1no1 AND bit1no2; // check if there is any carry generated out of the two bits

Totasum = (totasum | (sum << i)); // left shift the result to get it to the correct bit position

}

Else if (carry > 0)
{

Sum = bit1no1 XOR carry; // Add the carry to the first bit
Carry = bit1no1 AND carry; // save the new carry if generated out of this addition
Sum = Sum XOR bit1no2; // add this new sum to the second bit
Carry = Sum AND bit1no2;
Totasum = (totasum | (sum << i)); // left shift the sum to put it to correct bit position and then OR it with the result.

}

}
Return Totasum;

}