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2's Complement Binary Numbers

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Binary Addition

We need a brief aside. For straight binary numbers, addition works just as one would expect using place value. 0 + 0 = 0 (no surprise). 0 + 1 = 1 + 0 = 1. In binary, there is no way to have a displayed number other than 0 or 1, so 1 + 1 = 0 (in the 1's place) with 1 carried to the next most significant place (the 2's place). This is just like base 10 where 9 + 9 = 18; we have 8 in the 1's place, and the extra 10 gets carried one column to the left. What if we make thing a little more complicated?

10 + 01 = 01 + 10 = 11 (in base 10, 2 + 1 = 1 + 2 = 3)

10 + 10 = 100 (or, in base 10, 2 + 2 = 4)

   
 

 

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