half precision floating point multiplication
When multiplying floating points:


we add the (real) exponents, to get the output exponent
we multiply the two mantissas (remember the implied 1), round and shift as necessary. 


So the new exponent is $E=(19-15) + (3-15)= -8$.

The multiplication of the mantissas give
$$1.0011110111_2  \times = 1.0010011000_2 = 1.01101100111010101$$

taking only 10 digits (rounding down, see here) we get 
$M= 0110110011$.

The sign is a minus.

So the output is
$Out= 1\ 00111\ 0110110011$.

For sanity check, let's convert to decimal and see that it makes sense.

$A = (-1)^0 \times 2^{4} \times 1.2412109_{10} = 19.8593744$

$B = (-1)^1 \times 2^{-12} \times 1.1484375_{10} = -0.0002804 $

Then,

$A\cdot B = -0.0055686$

We can convert $Out$ from above to decimal, and get 
$Out = (-1)^1 \times 2^{-8} \times 1.4248047 = -0.0055656$ and the error is $0.000003 \approx 2^{-18}$ which makes sense (since the real exponent is $2^{-8}$ and we have a 10 digit significand)



See also https://oletus.github.io/float16-simulator.js/  for a calculator, and https://en.wikipedia.org/wiki/Half-precision_floating-point_format or https://en.wikipedia.org/wiki/Floating_point for definition and some more explanations.