GATE CS 2020 Q21 — Memory Hierarchy: Cache, Main Memory and Secondary Storage

To find the average memory access time, we first determine the number of words in a cache block and the total miss penalty.

1. Calculate the number of words per block:

• Block size = $256$ bytes
• Word size = $64\text{ bits} = 8\text{ bytes}$
• Number of words per block = $\frac{256}{8} = 32$ words

2. Calculate the miss penalty (time to fetch a block):

• Time for the $1^{\text{st}}$ word = $20$ ns
• Time for the remaining $31$ words = $31 \times 5 = 155$ ns
• Total miss penalty ($T_{\text{miss}}$) = $20 + 155 = 175$ ns

3. Calculate the Average Memory Access Time ($T_{\text{avg}}$):

Depending on how the cache and main memory are accessed, there are two standard interpretations:

• Interpretation 1 (Hierarchical Access): $$T_{\text{avg}} = T_c + (1 - H) \times T_{\text{miss}}$$ $$T_{\text{avg}} = 3 + 0.06 \times 175 = 3 + 10.5 = 13.5\text{ ns}$$
• Interpretation 2 (Simultaneous/Overlap Access): $$T_{\text{avg}} = H \times T_c + (1 - H) \times T_{\text{miss}}$$ $$T_{\text{avg}} = 0.94 \times 3 + 0.06 \times 175 = 2.82 + 10.5 = 13.32 \approx 13.3\text{ ns}$$

Both 13.3 ns and 13.5 ns are accepted correct answers.