In which of the following addition problems (using two’s complement notation) does an overflow error occur?

Question

In which of the following addition problems (using two’s complement notation) does an overflow error occur?

a) 0011+ 1010

b) 0100+ 0100

c) 1100+ 1100

Answer 1

In two's complement notation, an overflow error occurs when the sum of two positive numbers yields a negative result, or when the sum of two negative numbers yields a positive result. This happens because the most significant bit (MSB) is used to represent the sign of the number in two's complement notation: a '0' represents a positive number and a '1' represents a negative number.

Let's analyze each of the options:

a) 0011 (3 in decimal) + 1010 (-6 in decimal) = 1101 (-3 in decimal). No overflow occurs here because the sum of a positive number and a negative number will not result in an overflow.

b) 0100 (4 in decimal) + 0100 (4 in decimal) = 1000 (-8 in decimal). An overflow occurs here because the sum of two positive numbers yielded a negative result.

c) 1100 (-4 in decimal) + 1100 (-4 in decimal) = 1000 (-8 in decimal). No overflow occurs here because the sum of two negative numbers yielded a negative result.

So, the overflow error occurs in option b) 0100 + 0100.