Patterns that Add to Zero

Minus one added to plus one gives zero. If a particular bit pattern when added to one results in the pattern that represents zero, then it can represent minus one.

  11111 111
   0000 0001  =    110
   1111 1111  =   -1 
   0000 0000  =    010

There is a carry out of one from the high order column, but that is fine in this situation. The binary addition algorithm correctly applied gives the correct result in the eight bits. Look at another interesting case:

  11111 11
   0000 1110  =   1410
   1111 0010  =    ? 
   0000 0000  =    010