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Sum Property

Given integers x and y such that x, y, and x+y are representable as n-bit two's-complement numbers,


where tex2html_wrap_inline749 and tex2html_wrap_inline751

The sum property means that hardware adders can be built without regard to the interpretation -- signed or unsigned -- of the bit vectors being added. This is true when the lengths of the bit vector output is the same a both input bit vectors. When the sum is not representable we say that overflow or underflow has occurred.

Stephen W. Nuchia
Mon Dec 11 17:02:42 CST 2000