Question

In your implementation of the ALU there is no need to detect or handle overflow. However, it's a good mental exercise to think about when/how an overflow might occur. When adding numbers with different signs, overflow cannot occur because the sum must be no larger than one of the numbers. What happens when the signs of the numbers are the same? What happens in the case of subtraction? How do we detect when an overflow does occur?

Answer 1

1. An overflow has occurred in addition In addition, if any two 2's complement numbers are added, . When two different sign numbers are added overflow never occurs But both have the same sign (both positive or negative) then the overflow occurS The overflow occurs when the signs of the numbers are the same. Consider the below example: To add -6 and -7 (-6) 1010 +(-7) 1001 (-13) 0011 will be +3 represents overflow. Because the largest negative number with 3 bits is -8 2. An overflow has occurred in subtraction In subtraction, when two 2's complement numbers are subtracted, . Overflow occurs when the signs of the two numbers are different . Overflow cannot occur when the signs of the two numbers are same Consider the below example: Subtract -4 and 8 (whose signs are different) 11100 +11000 (-8) 110100 (-12) -4

The overflow occurs in the above example because the signs of the two numbers are different. Consider the below example: Subtract -2 and -9 (whose signs are same) 11110 2) +01001 (+9) 10011 (+7) The overflow occurs in the above example because the result of the subtraction is positive and is not same as the sign of the numbers 3. The following way explains how to detect an overflow: * First, check at the sign bits of the two Most Signiant Bits (MSB) n compare the sign bits to the sum. To detect when an overflow does occur in the following two situations: Consider that two negative numbers a and b have sign bits with value 1. The sum of the two negative numbers has sign bit 0 then adding two negative numbers has resulted in a non-negative, which means the overflow has occurred Consider that two negative numbers a and b have sign bits with value 0. The sum of the two non-negative numbers has sign bit 1 then adding two non-negative numbers has resulted in a negative, which means the overflow has occurred . .