Registers inside a CPU are the fastest memory but their number is very small. The main memory size is large, but it takes about one order of magnitude longer to access a memory location. To increase effective memory access speed, a smaller but faster memory known as cache memory is placed between registers and main memory. In modern computer systems, there are several levels of cache memories. For this problem it is assumed that a computer system has only one level of cache memory. Cache memory can be thought as an scratch$-$pad, where contents of some parts of the main memory resides for faster access. Different mapping schemes are used to map contents of the main memory to the cache. $($a$)$ What are the three cache mapping schemes? $($b$)$ Compare and contrast the advantages and disadvantages of these mapping schemes?