Issues of overflow and carry. (Using an 8-bit signed number storage).

   01111111  127
 + 00000001    1
   --------
   10000000  128 (unsigned) or -128 (signed and wrong)


  Overflow - when the result is larger than the storage unit. 
    (like carry for unsigned values).

    Overflow occurs when operands have same sign but sum has opposite sign.

     No Overflow, operands have different signs
     -1 + 127

       1111 1111   -1
     + 0111 1111  127 
      ----------
     1 0lll lll0  126

       signs of operands don't match - good result.
       # The carry flag will be set. The programmer chooses to ignore.

     No Overflow, operands have same sign but so does sum.


   Possible overflow.

     Sign bits match - good result. carry set. The carry is ignored.

       -1 + -1

       1111 1111   -1
     + 1111 1111   -1
      ----------
     1 1111 1110   -2


     Overflow occurs, signs match but result has different sign.

       -127 + -3    0111 1111  127    0000 0011  3   (absolute value)
                    1000 0000         1111 1100      flip
       1000 0001            1                 1      add 1
     + 1111 1101    1000 0001         1111 1101      2's complement
      ----------            
     1 0111 1110
       ^
       Sign change

       Overflow flag set.

       0111 1110  = 126  Should be -130 

     Similarly, two positives with a sum > 127 would create a sum with the 
     high bit set or a negative number.


   Most CPUs implement an overflow flag for this.
     Along with firmware routines for handling.
       Intel x86 - INTO (interrupt if overflow) 

     Signed and unsigned storage is flagged by CPU but user chooses how to 
       process results with appropriate code. 

Overview