# Multiplication of two binary numbers in fixed point arithmetic

So I'm performing some operations with fractional numbers in a 16-bit FIXED-POINT processor.

I have to multiply the numbers $$\ x=-6.35$$, represented in $$\ Q_{11}$$, and $$\ y=-0.1$$, represented in $$\ Q_{14}$$.

First I represent the numbers in the respective notation in binary. The MSB is the sign bit.

So $$\ x=11001.10100110011$$ and $$\ y=11.11100110011001$$. I know the binary point is just in our mind and the processor treats this numbers as integers.

Ok then we multiply the numbers and get $$\ x*y=11001000000100010011111001111011$$. We elimnate the repeated sign bit and save the 16 MSB and represent the result in the appropriate format $$\ Q_{10}$$: $$\ x*y=100100.0000100010$$. This number corresponds to $$\ - 27.966796875$$. But this doesn't make any sense, the result should be $$\ 0.635$$.

What is going on here? Why is the result different? Am I missing something?