Why do I get a negative number by multiplying two

I had an assignment where i had the following code excerpt:

/*OOOOOHHHHH I've just noticed instead of an int here should be an *short int* I will just left it as it is because too many users saw it already.*/

int y=511, z=512;

y=y*z;

printf("Output: %d\n", y);

Which gives me Output: -512. In my assignment I should explain why. So i was pretty sure it is because of the implicit conversion( correct me if I'm wrong:) ) happening from assigning an int value to an short int. But my tutor said that thing just happened called something with "triple round" i guess. I couldn't find anything about it and I'm watching a this video and the guy explains(25:00) almost the same thing I told my tutor.

Edit:

Here is my full code:

#include <stdio.h>

int main() {

    short int y=511, z=512;

    y = y*z;

    printf("%zu\n", sizeof(int));
    printf("%zu\n", sizeof(short int));

    printf("Y: %d\n", y);


    return 0;
}

Here is how i compile it:

gcc -pedantic -std=c99 -Wall -Wextra -o hallo hallo.c

I get no errors and no warnings. But if i compile it with -Wconversion flag enabled as follows:

gcc -pedantic -std=c99 -Wall -Wextra -Wconversion -o hallo hallo.c

I get the following warning:

hallo.c: In function ‘main’:
hallo.c:7:7: warning: conversion to ‘short int’ from ‘int’ may alter its value [-Wconversion]

So the conversion does happen right?

The conversion from int to short int is implementation defined. The reason you get the result you do is that your implementation is just truncating your number:

  decimal  |         binary
-----------+------------------------
    511    |       1 1111 1111
    512    |      10 0000 0000
 511 * 512 | 11 1111 1110 0000 0000

Since you appear to have a 16-bit short int type, that 11 1111 1110 0000 0000 becomes just 1111 1110 0000 0000, which is the two's complement representation of -512:

 decimal |     binary (x)      |         ~x          |    -x == ~x + 1 
---------+---------------------+---------------------+---------------------
   512   | 0000 0010 0000 0000 | 1111 1101 1111 1111 | 1111 1110 0000 0000