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Can a variable be both const and volatile?

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yes, the const means that the variable cannot be assigned a new value. The value can be changed by other code or pointer. For example the following program works fine. 

#include <stdio.h>
int main(void)
{
    const volatile int local = 10;
    int* ptr = (int*)&local;
    printf("Initial value of local : %d \n", local);
    *ptr = 100;
    printf("Modified value of local: %d \n", local);
    return 0;
}
...