Question

Assume a two-level inclusive cache hierarchy, L1 and L2, where L2 is the larger of the two. Consider the following statements:
\[ S_1:\ \text{Read misses in a write-through L1 cache do not result in writebacks of dirty lines to the L2.} \] \[ S_2:\ \text{Write allocate policy must be used in conjunction with write-through caches and no-write allocate policy is used with writeback caches.} \] Which of the following statements is correct?

• A. \(S_1\) is true and \(S_2\) is false
• B. \(S_1\) is false and \(S_2\) is true
• C. \(S_1\) is true and \(S_2\) is true
• D. \(S_1\) is false and \(S_2\) is false

Hint:

Write-through caches never have dirty blocks; policy pairings like write-allocate are common but not compulsory.

Answer 1

The Correct Option is A

Step 1: Evaluate Statement \(S_1\).
In a write-through L1 cache, every write is immediately propagated to the lower-level cache (L2). Therefore, L1 cache lines are never dirty. Hence, on a read miss in L1, there cannot be any dirty line to write back to L2. Thus, statement \(S_1\) is true.

Step 2: Evaluate Statement \(S_2\).
Write allocate and write no-allocate policies are design choices and are not mandatory combinations with write-through or writeback caches. Although write-through caches are commonly paired with no-write allocate and writeback caches with write allocate, this is not a strict requirement. Hence, statement \(S_2\) is false.

Step 3: Conclusion.
Since \(S_1\) is true and \(S_2\) is false, the correct option is (A).