A memory management system has 64 pages with 512 bytes page size. Physical memory consists of 32 page frames. Number of bits required in logical and physical address are respectively :
15 and 14
In paging, an address is split into a page (or frame) number and an offset within the page. The offset needs \(\log_2(\text{page size})\) bits; the page number needs \(\log_2(\text{number of pages})\) bits for a logical address, and the frame number needs \(\log_2(\text{number of frames})\) bits for a physical address.
Step 1 — Offset: page size 512 bytes \(= 2^{9}\), so 9 offset bits.
Step 2 — Logical address: 64 pages \(= 2^{6}\), so \(6 + 9 = 15\) bits.
Step 3 — Physical address: 32 frames \(= 2^{5}\), so \(5 + 9 = 14\) bits.
“14 and 15” gives the two values in reverse order; “14 and 29” and “16 and 32” do not follow from the page size, page count or frame count.
15 and 14 option is correct.
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