Adding two negative twos complement

Question

So let's say I want to add -7 and -7 together using 2s complement binary notation. I tried this:

-7 -> -00000111 -> 11111001
  1 1 1 1 1 0 0 1
+ 1 1 1 1 1 0 0 1
__________________
1 0 0 0 0 0 0 1 0

But after removing the extra digit, I get 00000010 = 2 instead of 11110001 = 14. What did I do wrong?

paxdiablo · Accepted Answer · 2013-01-30 04:02:14Z

5

Somewhere along the line, you lost (and kept losing) the carry flag:

          +- Here, 1 + 1 = 0 and sets carry to 1
          |   (everything up to here isokay).
          v
  1 1 1 1 1 0 0 1
+ 1 1 1 1 1 0 0 1
__________________
1 1 1 1 1 0 0 1 0
| | | ^ ^
| | | | |
| | | | +- Here, 1 + 1 + carry(1) is 1, not 0.
| | | +--- Ditto.
| | +----- And again.
| +------- Now it's just getting tedious.
+--------- Lastly, here is the final carry, just discard.

Negating 11110010 (invert bits and add 1) gives you 00001110, which is definitely 14 (8 + 4 + 2).

edited Jan 30, 2013 at 4:02

answered Jan 30, 2013 at 3:55

paxdiablo

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1 Comment

slowboat152 Over a year ago

Dang, that's a pretty basic mistake. Thanks a lot

SecurityMatt · Accepted Answer · 2013-01-30 03:54:36Z

1

Your math is wrong. Adding the 1 + 1 in position 5 gives you 10, so carry the 1. On the next column you need to add 1 + 1 + the carry, = 11 = 1 + a carry.

When you take this into account you end up with 1 1 1 1 0 0 1 0 = -14.

answered Jan 30, 2013 at 3:54

SecurityMatt

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