> For the complete documentation index, see [llms.txt](https://samypesse.gitbook.io/how-to-create-an-operating-system/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://samypesse.gitbook.io/how-to-create-an-operating-system/chapter9.md).

# Memory management: physical and virtual

The kernel knows the size of the physical memory available thanks to [GRUB](/how-to-create-an-operating-system/chapter-3.md).

In our implementation, the first 8 megabytes of physical memory will be reserved for use by the kernel and will contain:

* The kernel
* GDT, IDT et TSS
* Kernel Stack
* Some space reserved to hardware (video memory, ...)
* Page directory and pages table for the kernel

The rest of the physical memory is freely available to the kernel and applications.

![Physical Memory](/files/-LYkbouNZMvh8eAi4rjs)

## Virtual Memory Mapping

The address space between the beginning of memory and `0x40000000` address is the kernel space, while the space between the address `0x40000000` and the end of the memory corresponds to user space:

![Virtual Memory](/files/-LYkbouP-kv2KCGLnCwM)

The kernel space in virtual memory, which is using 1Gb of virtual memory, is common to all tasks (kernel and user).

This is implemented by pointing the first 256 entries of the task page directory to the kernel page directory (In [vmm.cc](https://github.com/SamyPesse/How-to-Make-a-Computer-Operating-System/blob/master/src/kernel/arch/x86/vmm.cc#L204)):

```cpp
/* 
 * Kernel Space. v_addr < USER_OFFSET are addressed by the kernel pages table
 */
for (i=0; i<256; i++) 
    pdir[i] = pd0[i];
```


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