figure out the logic of the overflow bit during addition. Remember that the overflow bit is 1 if the result of the output is out of range for a two's complement representation of the number. This occurs when the sign of the two inputs are the same, and the sign of the output differs from that of the inputs. With this in mind, you can determine if overflow occurred just by looking at the uppermost bits of the inputs and the output. 

Inputs: R (the leftmost bit of the result), A (the leftmost bit of the first operand), B (the leftmost bit of the second operand) Output: V (whether or not overflow occurred) 

R A B | V _________ 2a)0 0 0 | 2b)0 0 1 | 2c)0 1 0 | 2d)0 1 1 | 2e)1 0 0 | 2f)1 0 1 | 2g)1 1 0 | 2h)1 1 1 | Unoptimized sum of products equation: 2i) V = 

Draw the K-map and simplify Optimized sum of products equation: 2j) V =