Ones' Complement

Another system representation of negative numbers is ones' complement.

"Ones' complement" because a negative number is a "complement" to its positive counterpart up to 1. That is, if you add, bit by bit, the number and its negative counterpart, you get 11..111₂.

To find negative counterpart, simply invert all bits of a given positive number.

Ones' complement form of 01101100₂(99₁₀) is 10010011₂(-99₁₀). If you add this two numbers, you get 1 in all bits.

 01101100   99
+    
 10010011  -99
 ---------
 11111111

But this is just a clarification of the term "ones' complement".

To add two numbers represented in this system, you need:

1. Find counterpart
2. Add bit by bit (not forget about carry)
3. If occurred do the end-around carry

Example: Add +2₁₀ and -1₁₀

    binary   decimal
  00000010    +2
+ 
  11111110    -1
  --------    --
1 00000000     0    incorrect
+
         1          add carry
  --------    
  00000001    +1    correct

Limitations

• two zeros

From: Signed Number Representation (Wikipedia)