Question

If the frame size is 1024 , what is the physical address associated with the logical address \(<2,85>\) ?

Short answer

The physical address is 2133.

Step-by-step solution

Understanding the Problem

The logical address given is \(<2,85>\). This means that \(2\) is the page number and \(85\) is the offset. The frame size provided is \(1024\). Our task is to find the physical address associated with this logical address.

Calculating the Physical Address

The physical address can be calculated using the formula: \[ \text{Physical Address} = \text{(Page Number)} \times \text{(Frame Size)} + \text{Offset} \]Using the given values, the physical address = \(2 \times 1024 + 85 = 2048 + 85 = 2133\).

Verifying the Solution

To ensure that the computation is correct, recalculate each portion:\(2 \times 1024 = 2048\) and add \(85\), which gives \(2133\). The calculated physical address is consistent with our earlier computations.

Key concepts

Logical Address

When dealing with memory management in computing, a **logical address** refers to the address given by the CPU during the execution of a program. It is an abstract address at the application level, which is translated to a physical address by the Memory Management Unit (MMU). This translation ensures that the application can access the memory correctly without worrying about specific locations in the physical RAM.

In the example of the logical address given as \(<2,85>\), the value \(2\) represents the **page number**, while \(85\) denotes the **offset**. The logical address is a crucial concept because it allows for efficient memory management and protection by separating the user's view of memory from the actual physical memory addresses.

Frame Size

The **frame size** is a fixed length block of physical memory into which the operating system maps a page of logical memory. It is an essential component in the process of paging, which divides memory into equal-sized pages and frames.

Understanding frame size is vital because it helps determine how data is organized in memory and affects the efficiency of memory access. In the provided exercise, the frame size is given as \(1024\). This size means each page can fit into a frame of 1024 bytes, and it is the backbone for calculating the equivalent physical addresses when translating logical addresses.

Offset

The **offset** is the part of the logical address that identifies the precise position within a page. When a logical address is given as \(<2,85>\), the offset \(85\) indicates a specific location within the page number \(2\).

Offsets are crucial because they allow you to find the exact byte or word in a page. Once the frame is identified using the page number, the offset helps in pinpointing the exact location within that frame. This concept ensures that small data segments can be reached and manipulated quickly and with precision, enhancing the overall processing speed.

Page Number

In memory management, the **page number** refers to a part of the logical address that identifies which page is being accessed. Pages are equal-sized segments of memory, and each has a unique number associated with it.

In our problem example, the logical address \(<2,85>\) begins with the page number \(2\). This number directs the system to the specific frame allotted for page number \(2\). Coupling this with the offset \(85\), the system can determine the specific byte location within that frame.

• Helps in mapping logical pages to physical frames
• Divides memory into manageable and secure segments
• Makes the process of locating data easier and more intuitive

By using the page number in the translation process, we achieve better control and efficiency in memory use.