An Elementary Treatise on the Differential Calculus Founded by John Minot Rice, William Woolsey Johnson

By John Minot Rice, William Woolsey Johnson

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32 Directory states. 19 The Exclusive state (E) combines properties of Modified (M) and Shared (S). The E state allows silent upgrades to M, allowing the processor to write the block without communicating this fact to memory. It also allows silent downgrades to I, allowing the processor to discard its copy with notifying memory. The memory must have a way of inferring either of these transitions. In a directory-based system, this is typically done by having the directory assume that the node is in state M and forwarding all misses to that node.

1000 + 250 × 8 + 2000 × 8 + 150 × 56 = 27,400 e. A write-only workload must update both mirrors. Therefore, the IOPS is 28 × 285 IOPS = 7980 IOPS. 23 For reliability, we want as few components as possible; with larger disks, we are able to use half as many disks. Therefore, our system will now contain a total of 28 disks; we will have 4 enclosures and 4 controllers, each with a string of 7 disks. 24 a. 5 GB of data. We need only checksums to detect single errors (no correction here), and therefore need a 20-byte MD5 for every 4 KB of each file.

10 a. A 1 GB DRAM with parity or ECC effectively has 9-bit bytes and would require 18 512 Mb DRAMs. To create 72 output bits, each one would have to output 72/18 = 4 bits. b. A burst length of 8 reads out 32 bytes. c. 25, or 25% for reads to active pages. d. This is the scenario given in the figure. This requires 12 cycles of a 266 MHz clock, or 12 × (1/266 MHz) = 45 ns. e. The latency to an already active bank is 8 clock cycles, versus 12 if a bank activate is required. 5, or 50% longer. 11 The costs of the two systems are $130 + $800 = $930 with the DDR2-667 DIMM and $100 + $800 = $900 with the DDR2-533 DIMM.

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