Consider a logical address space with 32 pages, how many bits must be used to represent the page number in the logical address?

Question:

Consider a logical address space with 32 pages of 1024 words, how many bits must be used to represent the page number in the logical address?

15 bits.

Explanation:

Given:

A logical address space has 32 pages of 1024 words.

To represent these 32 pages, 5 bits are needed. i.e

32 = 2⁵

Also, each page contains 1024 words. This means that 10 bits will be needed for addressing within each 1024-word page. i.e

1024 = 2¹⁰

The total number of bits is the sum of the number of bits required for the pages and the number of bits required for addressing within each 1024-word page. i.e

5 + 10 = 15.

Therefore, the logical addresses must be 15 bits.

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