1. **Problem Statement:** Calculate the average access time and efficiency of a memory system with the following specifications: - Cache memory access time = 60 ns - Main memory access time = 160 ns - Hit ratio of cache memory = 0.9 2. **Formula for Average Memory Access Time (AMAT):** $$\text{AMAT} = (\text{Hit Ratio} \times \text{Cache Access Time}) + ((1 - \text{Hit Ratio}) \times \text{Main Memory Access Time})$$ 3. **Calculate Average Access Time:** Substitute the given values: $$\text{AMAT} = (0.9 \times 60) + (0.1 \times 160)$$ $$= 54 + 16 = 70 \text{ ns}$$ 4. **Calculate Efficiency:** Efficiency can be defined as the ratio of the average access time of cache to the average access time of the memory system: $$\text{Efficiency} = \frac{\text{Cache Access Time}}{\text{AMAT}} = \frac{60}{70} = 0.8571$$ 5. **Interpretation:** The average access time of the memory system is 70 ns, and the efficiency of the cache memory is approximately 85.71%.