By Edward A. Bender

Applying a realistic, "learn by way of doing" strategy, this 1st-rate textual content fosters the improvement of the abilities past natural arithmetic had to manage and control mathematical versions. From a range of fields — together with technological know-how, engineering, and operations examine — come over a hundred reality-based examples. 1978 version. comprises 27 black-and-white figures.

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This does not seem to be the case. However, one method along these lines is as follows. If x is a signed integer, then x + 231 is correctly represented as an unsigned number, and is obtained by inverting the high-order bit of x. Signed overflow in the positive direction occurs if x + y 231—that is, if (x + 231) + (y + 231) 3 · 231. This latter condition is characterized by carry occurring in the unsigned add (which means that the sum is greater than or equal to 232) and the high-order bit of the sum being 1.

2007 09:41:27] y 0 2-12 Overflow Detection x>0 x 0 x > 0x7FFFFFFF ÷ y y < 0x80000000 ÷ x x < 0x80000000 ÷ y This test is awkward to implement because of the four cases. It is difficult to unify the expressions very much because of problems with overflow and with not being able to represent the number +231. The test can be simplified if unsigned division is available. We can use the absolute values of x and y, which are correctly represented under unsigned integer interpretation. The complete test can then be computed as shown below.

The term x y ensures the correct result (0 in the sign position) if x and y have opposite signs. Similar remarks apply to the case of subtraction (right column). The code executes in nine instructions on the basic RISC. It might seem that if the carry from addition is readily available, this might help in computing the signed overflow predicate. This does not seem to be the case. However, one method along these lines is as follows. If x is a signed integer, then x + 231 is correctly represented as an unsigned number, and is obtained by inverting the high-order bit of x.

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