Consider the addition of two signed 32bit numbers If a posit

Solution

a)Overflow occurs when negative number is greater than positive number.

for suppose we want to compute 2-3.

2 in binary form 010

3 in binary form 011

When adding two numbers, overflow occurs when the two operands have the same leftmost bit and the leftmost bit of the answer is different.

to do 2-3

2\'s complement of 3 given by 101

adding 010

101

____

111

left most one is overflow and 2\'s complement of 11 is 01(leftmost bit of answer is 0 which is different from left most bits of two operands) so the answer is -1

b)When the operands have differing leftmost bits, overflow cannot occur when adding them together because we are adding a positive number with a negative number which means we are actually subtracting. It implies that the result cannot be bigger than the operands. So there is no possibility of overflow in this case. The leftmost bit is frequently referred to as the Most Significant Bit (MSB for short).