Why Does Multiplying 15 and -7 in Signed Binary Result in -105?

[snoggerT]

15X-7

The Attempt at a Solution

- I can't seem to figure this one out for some reason. My first attempt, I used 1111(15)X1001(2's complement of 7), but I can't get the right answer. I believe that the answer should come out to be the 2's complement of 105 since the actual answer is -105, but I can't get that. Please help.

 

[Uraptor]

Your problem is due to the way in which you have defined your numbers. When using signed numbers the MSB is actually -8.

So, 1111 = -8+(7) = -1 and 1001 = -8+(1) = -7.

To get the correct answer you need to add another MSB such that the MSB now equals -16.

Then, 01111 = 15 and 11001 = -16 +(9) = -7.

To do the multiplication;

01111 X 11001 = 15X(-16) + 15X9 = -105.