Consider the use of multi-level hot-cold bits in implementing a replacement algorithm for a set-associative cache with 2p ways and S sets. This is an approximation of the LRU policy that marks the most recently assessed way as hot, and the other one as cold (for a 2-way set-associative cache). This mechanism can be extended to more than two ways by providing multiple levels of hot-cold bits. For example, for a 4-way cache the victim is determined as the cold way of the cold pair. Required:
a. What is the total number of hot-cold bits for each set in this cache?
b. What is the total number of hot-cold bits in the cache?
c. At the end of the fifth access in this sequence (to Way 1), what are the settings of the hot-cold bit?