Calculate The Physical Address If The Following Logical Addresses

What is memory addressing?

Memory addressing is the process of locating and accessing data in a computer's memory. Each piece of data is stored at a specific memory address, which is a unique identifier. There are two main types of addresses: logical (virtual) and physical.

Logical addresses are used by programs to reference memory locations. Physical addresses are the actual locations in the computer's memory hardware. The process of converting logical addresses to physical addresses is called address translation.

Logical vs. physical addresses

Logical addresses are generated by the CPU and used by programs. They are part of the virtual address space created by the operating system. Physical addresses are the actual locations in the computer's memory chips.

The key difference is that logical addresses are relative to the program's memory space, while physical addresses are absolute locations in the computer's memory. This separation allows for better memory management and protection.

How to calculate physical address

Calculating the physical address from a logical address involves several steps, including understanding the memory management unit's page tables and the address translation process. Here's a simplified overview:

1. Divide the logical address into page number and offset.
2. Use the page number to find the corresponding frame number in the page table.
3. Combine the frame number with the offset to get the physical address.

The page size is typically a power of two, such as 4KB or 8KB. The offset is the part of the address that identifies the specific location within the page or frame.

Example calculation

Let's walk through an example to illustrate how to calculate the physical address from a logical address. Assume we have the following:

• Logical address: 10101010 (binary)
• Page size: 4KB (2¹² bytes)
• Page table entry for page 5: Frame 7

Step 1: Divide the logical address into page number and offset.

Since the page size is 4KB (2¹² bytes), we use the lower 12 bits for the offset and the remaining bits for the page number.

For our example, the logical address is 10101010 (binary). Assuming 8 bits for the page number and 4 bits for the offset:

• Page number: 1010 (binary) = 10 (decimal)
• Offset: 1010 (binary) = 10 (decimal)

Step 2: Use the page number to find the frame number in the page table.

From the page table, page 10 maps to frame 7.

Step 3: Combine the frame number with the offset to get the physical address.

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

Physical Address = (7 × 4096) + 10 = 28672 + 10 = 28682 (decimal)

The physical address is 28682 in decimal, which is 11011111111010 in binary.

Common pitfalls

When calculating physical addresses from logical addresses, there are several common mistakes to avoid:

1. Incorrect page size: Using the wrong page size will lead to incorrect offset calculations.
2. Page table errors: Missing or incorrect entries in the page table can result in incorrect frame numbers.
3. Offset overflow: If the offset exceeds the page size, it will wrap around to the next page.
4. Endianness issues: Different systems may use different byte orders, which can affect address calculations.