The tricky point with this round-half-up algorithm arrives when we come to consider negative numbers. As a point of interest, the symmetric versions of rounding algorithms are sometimes referred to as Gaussian implementations. Note that the differences between unsigned, sign-magnitude, and signed binary numbers are introduced in our book How Computers Do Math (ISBN: 0471732788).

Once again, the differences between unsigned, sign-magnitude, and signed binary numbers are introduced in our book How Computers Do Math (ISBN: 0471732788).

The point is that some applications (and some mathematicians) would regard "up" as referring to positive infinity.

The related IEEE 854 standard generalizes the original IEEE 754 to cover decimal arithmetic as well as binary.

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