What is the average memory access time of a machine whose hit rate is 96%, with a cache access time of 3 ns and a main memory access time of 70 ns?
The correct answer and explanation is :
To calculate the average memory access time (AMAT) of a system, we consider both cache hits and cache misses. The formula is:
AMAT = (Hit Rate × Cache Access Time) + (Miss Rate × (Cache Access Time + Miss Penalty))
Given:
- Hit Rate = 96% = 0.96
- Cache Access Time = 3 ns
- Main Memory Access Time = 70 ns
First, calculate the miss rate:
- Miss Rate = 1 – Hit Rate = 1 – 0.96 = 0.04
Now, apply the values to the AMAT formula:
- AMAT = (0.96 × 3 ns) + (0.04 × (3 ns + 70 ns))
- AMAT = 2.88 ns + (0.04 × 73 ns)
- AMAT = 2.88 ns + 2.92 ns
- AMAT = 5.8 ns
Explanation:
In computer systems, the memory hierarchy consists of multiple levels, such as registers, cache, main memory, and secondary storage. Cache memory is a small, high-speed storage located close to the CPU, designed to store copies of frequently accessed data from the main memory. When the CPU needs data, it first checks the cache; if the data is present, it’s a cache hit, resulting in faster access. If the data isn’t in the cache, it’s a cache miss, and the system must access the slower main memory.
The average memory access time provides a metric for the efficiency of the memory system, balancing the speeds of cache and main memory accesses. A higher hit rate improves the AMAT, as more data accesses are serviced quickly by the cache. Conversely, a lower hit rate increases the AMAT due to more frequent accesses to the slower main memory.
In this scenario, with a 96% hit rate, the system efficiently utilizes the cache, resulting in a low average memory access time of 5.8 ns. This efficiency minimizes delays in data retrieval, enhancing overall system performance.