Given a system with TLB hit ratio h, memory access time m, and TLB lookup time t, which formula correctly represents the Effective Access Time (EAT)?

medium🪤 Complexity Trap Q5 of Q15

Operating Systems - TLB - Translation Lookaside Buffer & Effective Access Time

AEAT = h * (m) + (1 - h) * (2 * m + t)

BEAT = h * (t + m) + (1 - h) * (t + 2 * m)

CEAT = h * (t + m) + (1 - h) * (2 * m)

DEAT = h * m + (1 - h) * (t + m)

Step-by-Step Solution

Solution:

Step 1: Define components
h = TLB hit ratio, t = TLB lookup time, m = memory access time.
Step 2: Calculate EAT
On hit: time = TLB lookup + memory access = t + m.
On miss: time = TLB lookup + page table walk (memory access twice) = t + 2 * m.
EAT = h * (t + m) + (1 - h) * (t + 2 * m).
Step 3: Evaluate options
A: Incorrect -- TLB lookup time t is misplaced.
B: Incorrect -- misses second memory access.
C: Incorrect -- misses TLB lookup time on miss.
D: Correct -- matches the standard formula.
Final Answer:
Option B -> Option B
Quick Check:
Miss includes extra memory access and TLB lookup time [OK]

Quick Trick: Miss cost includes TLB lookup + 2 memory accesses [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Interviewer Note:

CONTEXT

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