Assume a logical address space of 64 pages of 2048 words, each mapped into a physical memory of 32 frames. You are required to calculate the following parameters related to paging.

No. of bits needed for p = ? bits

No. of bits needed for f =  ? bits

No. of bits needed for d =   ? bits

Logical address size =  ? bits

Physical address size =  ?  bits

Solution:

To calculate the parameters related to paging, let's analyze the given information:

Logical address space:

Number of pages (p): 64

Words per page: 2048

Physical memory:

Number of frames (f): 32

To determine the number of bits needed for each parameter, we can use the following formulas:

Number of bits needed for p = log2(p)

Number of bits needed for f = log2(f)

Number of bits needed for d = log2(words per page)

Logical address size = Number of bits needed for p + Number of bits needed for d

Physical address size = Number of bits needed for f + Number of bits needed for d

Let's calculate each parameter step by step:

Number of bits needed for p = log2(64) = log2(2^6) = 6 bits

Number of bits needed for f = log2(32) = log2(2^5) = 5 bits

Number of bits needed for d = log2(2048) = log2(2^11) = 11 bits

Logical address size = Number of bits needed for p + Number of bits needed for d

= 6 bits + 11 bits

= 17 bits

Physical address size = Number of bits needed for f + Number of bits needed for d

= 5 bits + 11 bits

= 16 bits

Therefore, the calculated parameters are:

No. of bits needed for p = 6 bits

No. of bits needed for f = 5 bits

No. of bits needed for d = 11 bits

Logical address size = 17 bits

Physical address size = 16 bits