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

The average access time is calculated using the formula: Average Access Time = (Hit Ratio) × (Cache Access Time) + (1 − Hit Ratio) × (Main Memory Time). Given a Hit Ratio of 0.98, Cache Access Time of 12 nsec, and Main Memory Access Time of 1.5 msec (1.5 × 10^6 nsec), the calculation is performed as: Average Access Time = (0.98) × (12) + (0.02) × (1.5 × 10^6). This simplifies to 11.76 + 30,000, resulting in an average access time of 30,011.76 nsec. The average access time is approximately 41.76 nsec.