Patterns that Add Up to Zero

The "binary addition algorithm" does NOT work with sign-magnitude. There are algorithms that do work with sign-magnitude, and some early computers were built to use them. (And other computers were built using other not-ready-for-prime-time algorithms). It took several years of experience for computer science to decide that a better way had to be found.

There is a better way. Recall a question and its answer from several pages ago:

  11111 111
   0000 0001  =   110
   1111 1111  =   ? 
   0000 0000  =   010