Calculate The Physical Address of The Following Logical Addresses

In computer systems, logical addresses are used by programs to reference memory locations, while physical addresses are the actual locations in RAM. The Memory Management Unit (MMU) translates logical addresses to physical addresses. This page explains how to calculate the physical address from a given logical address.

What is a physical address?

A physical address is the actual location of data in the computer's memory (RAM). It's a unique identifier that points directly to a specific memory cell. Physical addresses are used by the hardware to access memory locations.

In contrast, logical addresses are the memory references used by programs. These addresses are relative to the program's memory space and are translated to physical addresses by the operating system.

Logical vs. physical addresses

Logical addresses are virtual addresses that programs use to reference memory. They are relative to the program's memory space and don't correspond directly to physical memory locations.

Physical addresses are the actual locations in RAM where data is stored. The operating system and hardware use these addresses to access memory.

Key Difference

Logical addresses are program-specific and virtual, while physical addresses are hardware-specific and real.

Memory Management Unit (MMU)

The Memory Management Unit (MMU) is a hardware component that translates logical addresses to physical addresses. It uses page tables to perform this translation.

The MMU maintains a page table that maps logical page numbers to physical frame numbers. When a program accesses memory, the MMU uses this table to find the corresponding physical address.

Address translation process

The address translation process involves several steps:

Split the logical address into page number and offset
Use the page number to find the corresponding frame number in the page table
Combine the frame number with the offset to get the physical address

Address Translation Formula

Physical Address = (Frame Number × Page Size) + Offset

Example calculation

Let's calculate the physical address for a logical address of 0x1A3F, assuming:

Page size = 4KB (4096 bytes)
Page table entry for page 1 is frame 5

Step 1: Split the logical address into page number and offset

0x1A3F in binary is 0001 1010 0011 1111

Page number: 0001 1010 (0x1A)

Offset: 0011 1111 (0x3F)

Step 2: Find the frame number in the page table

Page 0x1A maps to frame 5

Step 3: Calculate the physical address

Physical Address = (5 × 4096) + 63 = 20480 + 63 = 20543 (0x504F)

Result

The physical address for logical address 0x1A3F is 0x504F.

FAQ

What is the difference between logical and physical addresses?: Logical addresses are virtual and program-specific, while physical addresses are real and hardware-specific.
How does the MMU translate addresses?: The MMU uses page tables to map logical page numbers to physical frame numbers.
What is the formula for address translation?: Physical Address = (Frame Number × Page Size) + Offset
Why is address translation important?: Address translation allows multiple programs to share memory safely and efficiently.
What happens if a page fault occurs?: The operating system loads the required page from disk into memory and updates the page table.