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/* Use test&set */
boolean test_and_set(boolean &mutex) {
  boolean tmp=mutex;   mutex=true;
  return tmp;
}
void mutex_init(boolean &mutex) { mutex=false;}
void mutex_lock(boolean &mutex) { while(test_and_set(mutex));}
void mutex_unlock(boolean &mutex) {mutex=false;}

/* Use swap&test */
boolean swap_and_test(boolean &a, boolean &b) {
   boolean tmp=a; a=b; b=tmp;
   return a;
}

void mutex_init(boolean &mutex) {mutex=false;}
void mutex_lock(boolean &mutex) {
    boolean wait=true;
    while(swap_and_test(&wait, &mutex)) {mutex=true;}
}
void mutex_unlock(boolean &mutex) {mutex=false;}

in Java:

Synchronized function or block would be an example of a mutex.

Not an example, I said 'implement' mutex.

The basic constructs of mutual exclusion are usually provided by hardware instructions. Operating system use these and provide types like mutex and condition variables.
Higher level mutual exclusion constructs are built on top of these.

your HW has to support an atomic read-modify-write instruction. Then u can implement a mutex. Other way around you has to be able to disable all the interrupts. Either way will work for you . The implementation itself is quite trivial.