Why do I get a negative number by multiplying two short ints?

Question

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          


        

Answer 1

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