Question

Whereas larger caches have lower miss rates, they also tend to have longer hit times. Assume a direct-mapped 8 KB cache has 0.22 ns hit time and miss rate ml; also assume a 4-way associative 64 KB cache has 0.52 ns hit time and a miss rate m2.

a. If the miss penalty is 100 ns, when would it be advantageous to use the smaller cache to reduce the overall memory access time?
b. Repeat part (a) for miss penalties of 10 and 1000 cycles. Conclude when it might be advantageous to use a smaller cache.

Answer 1

We compare the overall memory access time between a direct-mapped 8 KB cache and a 4-way associative 64 KB cache. The overall memory access time for the smaller 8 KB cache is significantly lower than the 64 KB cache.

Step-by-step explanation:

In this problem, we are comparing the overall memory access time between a direct-mapped 8 KB cache and a 4-way associative 64 KB cache. The hit time for the 8 KB cache is 0.22 ns and the hit time for the 64 KB cache is 0.52 ns. The miss penalty is given as 100 ns.

To calculate the overall memory access time, we need to consider both the hit time and the miss rate. If we assume that the miss rates (ml and m2) are the same for both caches, then we can compare the overall memory access times using the formula:

Overall access time = hit time + (miss rate * miss penalty)

Let's calculate the overall memory access times for both cache sizes:

For the 8 KB cache:
Overall access time = 0.22 ns + (0.22 * 100 ns) = 22.22 ns

For the 64 KB cache:
Overall access time = 0.52 ns + (0.52 * 100 ns) = 52.52 ns

From these calculations, we can see that the overall memory access time for the smaller 8 KB cache is significantly lower than the 64 KB cache.

Keywords: cache, hit time, miss rate, overall memory access time, direct-mapped, 4-way associative