1. Caches are important to providing a high-performance memory hierarchy to processors. Below is a list of 32-bit memory address references, given as word addresses: 3, 180, 43, 2, 191, 88, 190, 14, 181, 44, 186, 253 [6 pts] a. For each of these references, identify the binary address, the tag, and the index given a directmapped cache with 16 one-word blocks. Also list if each reference is a hit or a miss, assuming the cache is initially empty. Show all your work.

Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 5 < b < 10 using this index, in terms of the number of records n2 that satisfy this selection, as well as n1 and h defined above? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?