Question

Operating Systems

Name two differences between logical and physical addresses.

Why are page sizes always powers of 2?

Consider a logical address space of 64 pages of 1,024 words each, mapped onto a physical memory of 32 frames.
a. How many bits are there in the logical address?
  b. How many bits are there in the physical address?

Answer 1

Logical address is the virtual address generated by CPU to access the data while the physical address is the actual address at while data resides in the memory. Logical address space is limited by the number of bits in the address space of the CPU while the physical address is limited by the size of available main memory.

Page size is always powers of 2 because base of the binary number is 2 and hence for any given number of bits n for the address space, the total possible number of address that can be generate is 2ⁿ and this is the reason that to utilize entire possible address space, page size is kept in powers of 2.

a. Size of logical address in terms of number of words = 64*1024 = 2¹⁶ words

Hence number of bits for logical address = log₂ (number of words) = log₂ 2¹⁶ = 16 bits

b. Since size of frame = size of page = 1024 words

Size of physical memory = 32*1024 = 2¹⁵ words

Number of bits for physical address = log₂ 2¹⁵ = 15 bits

Please comment for any clarification.