$7.$ A system has a main memory with a read access time of $1800$ ns and uses a unified L$1$ cache.

The cache has a read hit ratio of $96\%.$ As you know, the purpose of the cache is to make the

main memory appear to have a shorter access time.

a$)(3)$ The cache, operating in look$-$aside mode, causes the system to appear to have an average

memory read access time of $430$ ns$.$ What is the cache read access time?

b$)(3)$ Suppose the cache operates instead in look$-$through mode and has an $85\%$ read hit ratio.

What cache read access time is required to make the system appear to have an average memory

read access time of $300$ nanoseconds