Digital Arithmetic

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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, ...