Question

these binary numbers in 2's complement is given
11010100 - 11101011 , perform the operation

what I did it negated 11101011 so I can perform addition and see if any overflow occur..

I've already did it and got 11101000 the problem is when you convert it to decimal it's -44-(-21) so it's -23 but my result is -24 !! , what's the problem ?

Answer 1

\[\begin{align*}11010100_2&=2^7+2^6+2^4+2^2\\
&=212_{10}
\end{align*}\]
\[\begin{align*}11101011_2&=2^7+2^6+2^5+2^3+2^1+2^0\\
&=235_{10}
\end{align*}\]
Then \(212-235=-23\).

Answer 2

I know that man please read my question again :(

Answer 3

Well you said you got -24, not -23.

Answer 4

That's why I asked , try solving it and I think you'll get the same result :( Am I missing something ? I think I solved it right but the final result wasn't

Answer 5

Hmm, I've never actually computed with negative binary numbers - what do you mean by negating the second number?

Answer 6

Well , I've read that when you're trying to check if an overflow occur you should add 2 numbers which will be in 2's complement and in my case it was a subtracting operation so i had to negate it.

Answer 7

you actually have to add one ? that's strange the question says it's already in 2's complement , my head hurts :( I think I should add one to fix this.

Answer 8

Yup it works after adding one. sorry for wasting your time.

Answer 9

After a quick search, I'm going to have to correct myself.
\[11010100=-(2^6+2^4+2^2)=-84 \]
\[11101011=-(2^6+2^5+2^3+2^1+2^0)=-107 \]
We're restricted to six bits, so we can go as high as \(0111111_2=+63_{10}\) and as low as \(1000000_2=-64_{10}\).

I haven't looked over the overflow aspect, but since you have it figured out...

And don't worry about it! Here to help any way I can.