Perform the given arithmetic operation on the following pairs of 8-bit 2’s complement numbers. In each case, indicate whether or not overflow occurs.

the numbers:

11010100 + 11101011

if I understood the question then the result is:

10111111 with a discard 1

and there's no overflow since the sign is the same " both are negative "

the problem is here:

11010100 - 11101011

how can I do this ?

negate the second one ? or what ? I think in 2's complement there should only be addtion to see if there's an overflow.

and since all the question have the same sign that got me

Question

Perform the given arithmetic operation on the following pairs of 8-bit 2’s complement numbers. In each case, indicate whether or not overflow occurs.

the numbers:

11010100 + 11101011

if I understood the question then the result is:

10111111 with a discard 1

and there's no overflow since the sign is the same " both are negative "

the problem is here:

11010100 - 11101011

how can I do this ?

negate the second one ? or what ? I think in 2's complement there should only be addtion to see if there's an overflow.

and since all the question have the same sign that got me

lyrae · Answer

11010100 + 11101011 is indeed 10111111 and one carry-bit.


If you write 11010100 - 11101011 in a clever way you realize it's actually the same as writing 11010100 + (-11101011).

Since -11101011 is signed and negative we have to calculate it's two's complement: -11101011 = 00010100 + 1 = 00010101.

This gives us 11010100 + 00010101 which is easier to calculate.


Please note that it's also possible to do binary subtraction by hand, but it's a bit more tricky.

anonymous · Answer

Oh , thanks for your help man ^^