Problem $5$

Consider a machine with the following characteristics:

The cache is $2-$way set associative with a block size of $128$ bytes and a total capacity of $512K$ bytes.

a$)$ The memory access time consists of an $10$ cycle latency $+1$ cycle per word in the block. When the cache is write$-$back, the replaced block is dirty $30\%$ of the time; the replaced block is written before reading the new block into the cache. There are no write buffers. What are the miss penalties for the following cache organizations?

$\backslash$table$[[,$Read Miss,Write Miss$],[$Write through, no write allocate,,$],[$Write through, write allocate,,$],[$Write back, write allocate,,$]]$

b$)$ Assume $60\%$ of the misses are cause by writes $($in all cache organizations$).$ If the data miss rate for the write through, no write allocate is $2\%,$ what must the miss rates for the write through, write allocate and write back write allocate situations be if all three cache organizations have the same average memory access time. The hit time is one cycle.