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Floating-Point Representation, Algorithms, and Implementations
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Guard Bits and Rounding
Because of the right shift of one of the operands during the alignment step, the
result of the addition/subtraction may have more fractional bits than the operands.
Moreover, during the normalization a left shift of the result might be performed.
Finally, during the rounding step these additional bits are disposed of and the
result has a significand of f fractional bits.
To get the correct final result after the normalization and rounding, a possi-
bility is to obtain all the fractional bits of the addition. However, ...