Comment on "Some New Results on Average Worst Case Carry"

When reading the above paper
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, the unwary person might easily come to the conclusion that "most carries are short." Actually, such a statement needs to be qualified. In fact, if a computer engineer designs an adder on this basis, he would probably find that the average add time is not as short as the theoretical analysis would lead him to expect. This is because Briley's analysis, and that of his predecessors Burks, Goldstine, and von Neumann [1], are both dependenent on the assumption that the numbers being added are evenly distributed among 2n possible bit combinations. In actual computation, most of the integers tend to have small magnitudes. Thus, a negative integer, if expressed in complement form, tends to have a long string of leading ones. When two such numbers are added, or when one of these is added to a positive integer giving a positive sum, a long string of carries would be generated. This means that in real computing situations the average carry might be much longer than Briley's analysis would indicate.