Addition

In 2’s complement, we perform addition the same as an addition for unsigned binary numbers. The only difference is here we discard the out carry i.e carry from MSB bit as long as the range lies within the accepted range for 2’s complement representation.

For eg: Consider a number of bits(n) = 4. So range of numbers will be -2^{n-1} \space to \space 2^{n-1} , i.e. -8 to 7.

x=2, y=3        
addition: 0010
          0011
          0101 
---> +5 in 4 bits

x=-2,y=-3     
addition: 1110
          1101
          1011 
---> -5 in 4 bits 
(discarding the out carry 1)

In the above examples, there was no overflow as the answers +5 and -5 lie in the range of -8 to 7.

Consider the example,

x=4, y=5        
addition: 0100
          0101
          1001 
---> -7 (not in range of -8 to 7)

Hence overflow occurs in the above example as -7 does not exist in the 4bits range.

For more details on overflow, you can refer to the following article Overflow in Arithmetic Addition in Binary Number System. 

We all know how to perform arithmetic operations of binary number systems. However, computer system generally stores numbers in 2’s complement format. So it becomes necessary for us to know how arithmetic operations are done in 2’s complement.