3.13.1 Operations performed on fixed-point integers behave the way one expects—t Computer Organizations and Design - Patterson

3.13.1 Operations performed on fixed-point integers behave the way one expects—the commutative, associative, and distributive laws all hold. This is not always the case when working with floating point numbers, however. Let’s first look at the associative law. The following table shows sets of decimal numbers. [20] <3.2, 3.5, 3.6> Calculate (A + B) + C by hand, assuming A, B, and C are stored in the modified 16-bit NVIDIA format described in 3.11.2 (and also described in the text). Assume 1 guard, 1 round bit, and 1 sticky bit, and round to the nearest even. Show all the steps, and write your answer in both the 16-bit floating point format and in decimal.


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