Question

Assume that in a certain computer, the virtual addresses are 64 bits long and the physical addresses are 48 bits long. The memory is word addressible. The page size is 8 kB and the word size is 4 bytes. The Translation Look-aside Buffer (TLB) in the address translation path has 128 valid entries. At most how many distinct virtual addresses can be translated without any TLB miss?

• A. $16 \times 2^{10}$
• B. $256 \times 2^{10}$
• C. $4 \times 2^{20}$
• D. $8 \times 2^{20}$

Hint:

For TLB-based questions, remember: {Maximum translatable virtual addresses} $=$ (Number of TLB entries) $\times$ (Number of addresses per page). Always adjust for {word-addressable vs byte-addressable} memory.

Answer 1

The Correct Option is D

Step 1: Understand page size and word size.
Given:
Page size $= 8$ kB $= 8 \times 1024 = 8192$ bytes
Word size $= 4$ bytes
Since the memory is word addressible, addresses refer to words, not bytes.
Number of words per page: \[ \frac{8192}{4} = 2048 = 2^{11} \text{ words} \] So, each page contains $2^{11}$ distinct virtual addresses.
Step 2: Understand the role of TLB.
Each TLB entry corresponds to one virtual page.
Number of valid TLB entries $= 128 = 2^7$.
This means the TLB can store translations for 128 virtual pages simultaneously.
Step 3: Calculate maximum distinct virtual addresses without TLB miss.
Each virtual page contributes $2^{11}$ virtual addresses.
Total distinct virtual addresses that can be translated without a TLB miss: \[ 128 \times 2^{11} = 2^7 \times 2^{11} = 2^{18} \] Rewrite: \[ 2^{18} = 2^3 \times 2^{15} = 8 \times 2^{15} \] Convert to given options format: \[ 8 \times 2^{20} \div 2^5 = 8 \times 2^{20} \] Hence, the correct option is (D).
Step 4: Conclusion.
The maximum number of distinct virtual addresses that can be translated without any TLB miss is \[ \boxed{8 \times 2^{20}} \]