Question

5.2 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

5.2.6 The formula shown in Section 5.3 shows the typical method to index a direct-mapped cache, specifically (Block address) modulo (Number of blocks in the cache). Assuming a 32-bit address and 1024 blocks in the cache, consider a diff erent

Answer 1

Solution:

Explanation:

=>We are using direct-mapped caching here.

=>We know that the formula to index the main memory block to the cache line number of cache memory.

= K mod N = P

Where K is the main memory block number, the mod is the modulus function, N is the number of cache lines and P is the cache memory line number where the main memory block is mapped.

Checking each block of main memory:

=>Number of cache lines = 1024

=>3 % 1024 = 3

Means block number 3 of the main memory will be mapped to cache line number 3 of cache memory.

=>180 % 1024 = 180

Means block number 180 of the main memory will be mapped to cache line number 180 of cache memory.

=>43 % 1024 = 43

Means block number 43 of the main memory will be mapped to cache line number 43 of cache memory.

=>2 % 1024 = 2

Means block number 2 of the main memory will be mapped to cache line number 2 of cache memory.

=>191 % 1024 = 191

Means block number 191 of the main memory will be mapped to cache line number 191 of cache memory.

=>88 % 1024 = 88

Means block number 88 of the main memory will be mapped to cache line number 88 of cache memory.

=>190 % 1024 = 190

Means block number 190 of the main memory will be mapped to cache line number 190 of cache memory.

=>14 % 1024 = 14

Means block number 14 of the main memory will be mapped to cache line number 14 of cache memory.

=>181 % 1024 = 181

Means block number 181 of the main memory will be mapped to cache line number 181 of cache memory.

=>44 % 1024 = 44

Means block number 44 of the main memory will be mapped to cache line number 44 of cache memory.

=>186 % 1024 = 186

Means block number 186 of the main memory will be mapped to cache line number 186 of cache memory.

=>253 % 1024 = 253

Means block number 253 of the main memory will be mapped to cache line number 253 of cache memory.

I have explained each and every step with the help of statements attached to it..