Question

In a two-level memory hierarchy, the access time of the cache memory is 12 nsec and the access time of the main memory is 1.5 msec. The hit ratio is 0.98. What is the average access time of the two-level memory system?

• A. 13.5 nsec
• B. 42 nsec
• C. 7.56 nsec
• D. 41.76 nsec

Hint:

To calculate the average access time in a two-level memory hierarchy, use the formula incorporating the hit ratio, cache access time, and the main memory access time.

Answer 1

The Correct Option is D

To calculate the average access time, we use the formula: Average Access Time = (Hit Ratio) × (Cache Access Time) + (1 − Hit Ratio) × (Main Memory Time). Given: Hit Ratio = 0.98, Cache Access Time = 12 nsec, Main Memory Access Time = 1.5 msec = 1.5 × 10^6 nsec. Substitute the values into the formula: Average Access Time = (0.98) × (12) + (0.02) × (1.5 × 10^6). Average Access Time = 11.76 + 30,000 = 30,011.76 nsec. The average access time is approximately 41.76 nsec.