Chapter 5 ½ Function and Performance 61
associated with the base packaging, power, and interface. The electronic selection follows a square law; a doubling of the selection circuitry provides access to a core stack that is 4 times larger. All other costs are roughly linear, although the manufacturing cost for larger stacks would probably follow some economy of scale due to the high setup cost of threading core memories.
Another point is that Grosch's law, derived from the definition of performance, is itself a definition. Consider Knight's model:
Let P equal the price of the memory on the system. Assume the use of a 2k x 1 memory chip and a memory system n bits wide, and further assume that the processor can use 100 percent of the memory data rate. To supply concrete cost and performance parameters we will use a 4-kiobit chip, which in 1978 cost about $25 and had a cycle time (at the processor) of about 500 ns. Then,
Thus, according to this performance model, Grosch's law holds by definition because
2 Processor performance is usually matched to memory size, as suggested
by Amdahl (see page 46).
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