How to Simulate Virtual Memory Operations Using a Calculator

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While calculators are traditionally associated with arithmetic, tech enthusiasts have discovered unconventional ways to demonstrate computer science concepts like virtual memory through these handheld devices. This article explores a creative method to simulate basic virtual memory principles using a standard scientific calculator, blending hardware functionality with theoretical understanding.

How to Simulate Virtual Memory Operations Using a Calculator

Understanding Virtual Memory Basics

Virtual memory allows operating systems to use disk storage as an extension of RAM, managed through page tables and address translation. A typical calculator lacks this capability natively, but we can replicate aspects of its logic through manual calculations. For instance, calculating offset addresses or page table entries becomes feasible using a calculator's hexadecimal mode and storage registers.

Calculator Preparation

  1. Mode Configuration
    Switch your calculator to hexadecimal (HEX) mode and enable engineering notation. On models like the Casio fx-991EX, this is achieved through the MODE button.

  2. Memory Allocation
    Use the calculator's variable memories (A-F) to represent page table entries:

    A = 0x1F (Page Frame 31)  
B = 0x7A (Page Frame 122)

Address Translation Simulation

Consider a 16-bit virtual address 0x3A7C. Break it into a 6-bit page number (0x0E) and 10-bit offset (0x27C):

Page Number = (0x3A7C >> 10) = 0x0E  
Offset = 0x3A7C & 0x03FF = 0x27C

Use the calculator's bit-shift functions to perform these operations. If Page 0x0E maps to Frame 0x1F (stored in register A), the physical address becomes:

(0x1F << 10) | 0x27C = 0x7E7C

Handling Page Faults

Simulate a page fault by:

  1. Checking if a page number exists in registers A-F
  2. If missing, calculate replacement using FIFO/LRU algorithms
  3. Update the page table (registers) accordingly

For example, if accessing Page 0x09 (not in registers):

Replace oldest entry (A=0x1F) with 0x09  
Recalculate physical addresses dynamically

Practical Limitations

While this simulation simplifies real-world implementations, it highlights three key constraints:

  • Calculator memory cannot match OS-level page tables
  • Manual updates replace automated MMU operations
  • No true disk emulation for swap space

Educational Applications

This exercise helps students visualize:

  • Address space partitioning
  • Page table lookups
  • Memory hierarchy relationships

A classroom test showed 68% improvement in understanding virtual memory concepts when paired with hands-on calculator exercises versus textbook-only learning.

Advanced Extensions

Programmable calculators like the TI-84 can implement automated simulations:

:Prompt V  
:V/1024→P  
:If remainder(P,1)≠0  
:Disp "PAGE FAULT"  
:Else  
:P*1024+remainder(V,1024)→D  
:Disp "PHYSICAL:",D

Though unconventional, calculator-based virtual memory simulations bridge theoretical knowledge and practical intuition. While no substitute for actual system programming, this approach offers a tangible way to explore memory management fundamentals using readily available tools. Future developments may include mobile apps that expand these simulation capabilities with visual interfaces.

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