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Signed integers (cont)

Twos complement: to form -X from X ... NEG all bits, then add 1

Now have only one representation for zero (00000000)

  • -0  =  ~00000000+1  =  11111111+1  =  00000000
Only one zero value.   Also, -(-x) = x

Even better,  x + -x = 0 in all cases with simple addition 

  00000011  3     00101010  42      01111111
+ 11111101 -3   + 11010110 -42    + 10000001
  --------        --------          --------
  00000000  0     00000000   0      00000000  0

Always produces an "overflow" bit, but can ignore this