Two's complement binary multiplication

Question

I'm confused about where I'm going wrong in the following problem using binary multiplication with two's complement.

I am trying to multiply 12 * -6.

We know that 12 = 01100 and -6 = 11010, and sign-extended we get 00000 01100 * 11111 11010. I tried multiplying these two numbers as follows:

     1111111010
   x 0000001100
   ------------
     0000000000
    0000000000
   1111111010
+ 1111111010
---------------
 10111110111000

This is definitely not -72, so what am I doing wrong?

Answer 1

Drop the digits from the left that don't fit in the data type:

10111110111000

truncates to

1110111000

You'll find that this is indeed -72.