Two's complement question.

Question

dan815 · Answer

hi, so instead of just giving you the trick to 2s compliment, do you understand how or why the 2s compliment is constructed?

curry · Answer

if it's positive, i just keep it the same. and if it's negative, i write the positive number, flip the bits, and add 1 right?

curry · Answer

I got 9 for both.

curry · Answer

is that right?

curry · Answer

well 131 can be represented with just 8, but wouldn't the first number represent negative and postive?

anonymous · Answer

for twos compliment notation, generally you add a single bit, but there is a special exception

curry · Answer

or do we not need to worry about signed magnitude arch?

anonymous · Answer

For example, for two bits we have:
00 = 0
01 = 1
10 = -2
11 = -1
Our range is -2 to 1, which is given by $-2^{n-1}$ to $2^{n-1}-1$.

anonymous · Answer

So 8 bits will support -128 to 127

curry · Answer

wait why is 10, -2?

curry · Answer

do we just subtract 1 and flip the bits?

anonymous · Answer

If you add $1+-2$, we have $01 + 10 = 11$  which is $-1$.

anonymous · Answer

It wraps around so that addition will still work.