# The bit representation of the hash multiplication method

In the CLRS image below, I don't understand why exactly $$h (k)$$ = the $$p$$ higher order parts of the lower w-bit Half of the product.

For context, this is supposed to compute
$$h (k) = lfloor m (k A ; text {mod} 1) rfloor$$

For more context, CLRS mentions the following, but I still don't understand why those $$p$$ higher order The bits are what we are looking for.