Memory Management - Virtual To Physical Address Translation

Please I need the correct way to convert Logical (Virtual) Address to Physical Address , i have the following Question :

Given the following Page Table :

Knowing that the virtual pages and physical frame are 1 k Bytes, what is the memory address corresponding to each of the following virtual addresses encoded in hexadecimal: 142A and 0AF1?

i solved it like this , but i don't know if it is correct :

142A (hex)=5162(decimal)

5162/1024=5 (page number ) <----> Frame 1 in page table

5162mod1024=42 (Offset)

so the physical address corresponding to 142A = 1(physical)+42 (offset) or (1*1024+42)

so is that correct ?!

Kind regards

1 Answer

1Kbytes = 1024 bytes. 1024₁₀ = 0400₁₆

• page 0 = 0000₁₆, page 1 = 0400₁₆, page 2 = 0800₁₆, page 3 = 0C00₁₆, page 4 = 1000₁₆, page 5 = 1400₁₆

  • So, 142A₁₆ is in page 5 ...

• Logical page 5 points to physical page 1. Each page is 0400₁₆ bytes. Physical page 1 starts at 0400₁₆ (page 0 would start at 0000₁₆).

• 142A₁₆ is 2A₁₆ bytes past the start of page 5 at 1400₁₆ ...

  • so you add 2A₁₆ to the starting address of physical page 1 which is 0400₁₆. So logical address 142A₁₆ really is physical address 042A₁₆.

  • Anything 1400₁₆ to 17FF₁₆ logically corresponds to 0400₁₆ to 07FF₁₆ physically, etc.

This is the type of table you could make to help you. All based on multiples of 0400₁₆ since that is the page size.

Logical Page Number Logical Page Address -> Physical Page Number Physical Page Address 0 0x0000 - 0x03FF 4 0x1000 - 0x13FF 1 0x0400 - 0x07FF 6 0x1800 - 0x1BFF 2 0x0800 - 0x0BFF 8 0x2000 - 0x03FF 3 0x0C00 - 0x0FFF 9 0x2400 - 0x27FF 4 0x1000 - 0x13FF 12 0x3000 - 0x33FF 5 0x1400 - 0x17FF 1 0x0400 - 0x07FF