Computer Organization and Embedded Systems (6th Edition)

Chapter 9, Arithmetic problem 17P

[M]Tree reduction of summands using 3-2 and 4-2 reducers was described in Sections 9.5.3 and 9.5.4. It is also possible to perform 7-3 reductions on each reduction level. When only three summands remain, a 3-2 reduction is performed, followed by addition of the nal two summands. (a) How many 7-3 reduction levels are needed to reduce 32 summands to three? Compare this to the seven levels needed to reduce 32 summands to three when using 3-2 reductions. (b) Example 9.3 in Section 9.10 shows that log2k 1 levels of 4-2 reduction are needed to reduce ksummands to 2 in a reduction tree. How many levels of 7-3 reduction are needed to reduce ksummands to 3?

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