In a paging system, it takes 30 ns to search translation Look-a-side Buffer (TLB) and 90 ns to access the main memory. If the TLB hit ratio is 70%, the effective memory access time is :
147ns
With a translation look-aside buffer, every reference first searches the TLB. On a hit the frame number is obtained there and one memory access fetches the data; on a miss the page table in main memory must be read first, costing one extra memory access.
Step 1 — Hit time: \(30 + 90 = 120\ \text{ns}\).
Step 2 — Miss time: \(30 + 90 + 90 = 210\ \text{ns}\).
Step 3 — Weighted average: \(\text{EMAT} = 0.7 \times 120 + 0.3 \times 210 = 84 + 63 = 147\ \text{ns}\).
84 ns is only the hit contribution, 120 ns is the hit time alone, and 48 ns weights only the TLB search time on hits and a single memory access on misses (0.7 × 30 + 0.3 × 90).
147ns option is correct.
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