3 Thinking about the memory hierarchy In class, we discussed the computer storage hierarchy, and the fact the types of storage high in the pyramid given in Chapter 1 (e.g. registers, Ll cache, ...) are orders of magnitude faster than the types at its base (e.g. hard drives, optical storage, ...). Some access times are given for current hardware? . (Recall that the abbreviation ns is for nanoseconds and ms is for milliseconds.) So, looking at the table, we see for example if we'd like to read something stored in a L2 cache, it should take about a half of a nanosecond to fetch it, etc. access time location L1 cache L2 cache RAM hard drive DVD 0.5 ns 7 ns 100 ns 10 ms 140 ms In our every day lives, we're not used to dealing with units of time this small. To give us a sense of how much slower devices at the bottom of the pyramid are from the top, let's pretend instead that access times are in units to which we're more accustomed. Using the same ratios as we had in the table above, fill in the following fake access times. For example, in the table of real access times, we see that it takes 0.5 ns on average to read from a L1 cache, and 7 ns to read from a L2 cache. L2 caches are on average 14 times slower. If we pretend that it takes 1 second to read from an Ll cache, it would take 14 seconds to read from a L2 cache. Using this same procedure, fill in the rest of the table. fake access time 1 sec 14 sec location L1 cache L2 cache RAM hard drive DVD Now, let's do the same thing, but instead of time, let's consider distance. Pretend that we're baking a cake. We're doing all of our work on the kitchen counter, and different ingredients that we need for the cake are found in different storage places. If the Li cache is the cabinet two feet above the counter, the L2 cache would be 14 times farther away, so it's 28 feet away (maybe in our basement?). Using the same ratios as before, fill in the rest of the chart: fake distance 2 feet 28 feet location L1 cache L2 cache RAM hard drive DVD