A computer with cache access time of 100\,ns, a main memory access time of 1000\,ns, and a hit ratio of 0.9 produces an average access time of (i) 250

Question

A computer with cache access time of $100\,ns$, a main memory access time of $1000\,ns$, and a hit ratio of $0.9$ produces an average access time of

(i) $250\,ns$  
(ii) $200\,ns$  
(iii) $190\,ns$  
(iv) None of these

Accepted Answer

**Answer: (iii) 190 ns (simple); 200 ns hierarchical - both shown**

Given: $T_c=100\,ns$, $T_m=1000\,ns$, $h=0.9$, $miss=0.1$

*   **Simultaneous access (common textbook for this question):**
    $T_{avg}= h\cdot T_c + (1-h)\cdot T_m = 0.9	imes100 + 0.1	imes1000 = 90+100 = 190\,ns$ → **Option (iii)**

*   **Hierarchical access (cache checked first, then memory on miss):**
    $T_{avg}= h\cdot T_c + (1-h)\cdot(T_c+T_m) = T_c+(1-h)T_m = 100+100 = 200\,ns$ → **Option (ii)**

Most WBUT/MAKAUT PYQs expect **(iii) 190 ns**. If hierarchical model is assumed, answer is **200 ns**.

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