Write a simple C program for which a $4-$way associative cache has a significantly lower miss rate than an equally sized $2-$way set associative cache. It will be easiest if you use blockSize$1.$c as a starting point. You may choose any cache size and block size you wish, but they must remain the same for the entire problem.

Hints for writing programs with a specified cache behavior:

You need not loop through the entire array. Instead, find addresses that collide in the cache. Remove the inner loop and make NUM$\_$LOOPS $1,000,000.$Notice in blockSize$1.$c that array is an array of characters; therefore, each item in the array is exactly $1$ byte. As a result, it is easy to identify data items that will or will not conflict in the cache. For example, in an $8$KB direct$-$mapped cache, array bytes $0$ and $8192$ will conflict. This is basically a pencil$-$and$-$paper problem that we happen to be using a cache simulator to verify.Write the simplest program you can that will produce a $100\%$ miss rate for the $2-$way cache.

Submit the source code, all cache parameters, and resulting hit rates.