Topic: GPU Virtual memory

If an address space uses only 48 bits, and a machine has a 1GB super page size, how many Virtual Page Numbers (VPN) can exist?

Question

Topic: GPU Virtual memory

If an address space uses only 48 bits, and a machine has a 1GB super page size, how many Virtual Page Numbers (VPN) can exist?

BlackTom AI · Accepted Answer

Virtual addresses are partitioned into a page offset (determined by page size) and a Virtual Page Number (VPN). The number of VPNs equals the total number of byte-addressable entries in the virtual address space divided by the page size.

Relevant concepts:
- Virtual address bits = VPN bits + page-offset bits.
- Page-offset bits = log2(page size in bytes).
- Number of VPNs = 2^(VPN bits) = (virtual address space size) / (page size).

Step-by-step reasoning and calculations:
1. Total virtual address space size = 2^48 bytes (since 48-bit addresses).
2. Page size = 1 GB. In binary addressing contexts 1 GB = 1 GiB = 2^30 bytes.
3. Page-offset bits = log2(2^30) = 30 bits.
4. VPN bits = total address bits − page-offset bits = 48 − 30 = 18 bits.
5. Number of VPNs = 2^(VPN bits) = 2^18.
6. Numeric check: 2^48 bytes = 281,474,976,710,656 bytes. Divide by 1,073,741,824 bytes (2^30) gives 262,144 pages = 2^18.

Why the correct answer is correct:
Because each VPN identifies one page and there are 2^18 distinct VPN values when 18 bits remain for the VPN. This follows directly from splitting 48 address bits into 30 offset bits (for 1 GB pages) and 18 VPN bits.

Why the other options are incorrect:
- 2^30 VPNs would imply VPN bits = 30, which would occur if page size were 2^18 bytes (256 KB), not 1 GB.
- 2^28 VPNs corresponds to VPN bits = 28 (would result from a 2^20 = 1 MB page size).
- 2^48 VPNs would be true only if page size were 1 byte (page-offset = 0 bits), which is not the case.

Conclusion: The correct number of VPNs is 2^18 VPNs, matching the provided answer.

Topic: GPU Virtual memory If an address space uses only 48 bits, and a machine has a 1GB super page size, how many Virtual Page Numbers (VPN) can exist? 单项选择题

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