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 $

enter the image description here


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.

enter the image description here