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, loworder bits are used to pick the memory module
when consecutive addresses are encountered. Since any combination of
loworder 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 threebit 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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 Spring '10
 CharlesB.Cameron
 Computer Architecture, CPU cache, main memory, Power of two

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