Why the address of variable of child process and parent process is same

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Because it’s a virtual address, not a physical one.

Each process gets its own address space (for example, a 32-bit system may allow each process to have its own address space with the full 4G range).

It’s the memory management unit that will map virtual addresses to physical ones (and handle things like page faults if swapped out pages need to be bought back in from secondary storage).

The following diagram may help, each section representing a 4K block of memory:

   Process A           Physical Memory      Process B
   +-------+           +-------------+      +-------+
0K |       |---->   0K |  (shared)   | <----|       | 0K
   +-------+           +-------------+      +-------+
4K |       |--+     4K |             | <----|       | 4K
   +-------+  |        +-------------+      +-------+
8K |       |  +->   8K |             |      |       | 8K
   +-------+           +-------------+      +-------+
       |                : : : : : : :           |
       |               +-------------+          |
       |          128K |             | <--------+
       |               +-------------+
       +--------> 132K |             |
                       +-------------+

You can see, in that diagram, the disconnect between virtual memory addresses and physical memory addresses (and the possibility for processes to share memory blocks as well). The addresses down the left and right sides are virtual addresses which the processes see.

The addresses in the central block are actual physical addresses where the data “really” is, and the MMU handles the mapping.

For a deeper explanation of fork (and exec), you may also want to look at this answer.

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