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Assignment09Fall2010Solution

# Assignment09Fall2010Solution - 525.412 Computer...

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525.412 Computer Architecture Assignment 9 Solutions 7.18 In the memory module interleaving scheme of Table 7.5, a speciﬁc system is to be delivered with six memory modules of 2 28 words each. What is the maximum amount of interleaving that can be used in this system? Solution With interleaving, low-order bits are used to pick the memory module when consecutive addresses are encountered. Since any combination of low-order bits can occur, we must set aside a number of bits, q , such that 2 q evenly divides the number of memory modules. In this case, we want 6 2 q = an integer. Therefore q = 1 . To see why, consider what would happen if we picked q = 2. To se- lect one of six modules requires a three-bit subset of all the address bits. With q = 2, the two least signiﬁcant address bits, bits a 1 and a 0 are involved in selecting a memory module. The third bit will be the most signiﬁcant bit, a 30 . Then address bits a 29 a 28 ...a 2 would be ap- plied to each memory module and decoded internally, while address bits a 30 , a 1 , and a 0 would be used to select one of the six available mem- ory modules. But these bits can occur in up to eight combinations, of which only six would be valid. Suppose the six valid combinations were a 30 a 1 a 0 ∈ { 000 , 001 , 010 , 011 , 100 , 101 } . There would be no problem when, say, a 30 = 0. But any address with

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Assignment09Fall2010Solution - 525.412 Computer...

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