Blending behaviour with transparence

I have an image with two layers.

The bottom layer is full red i.e. rgb = (255, 0, 0) and 100% opaque

The top layer is black (0, 0, 0) with opacity 50% and blend mode normal.

I expect and need the result to be exactly half way between black and red, i.e. rgb = (128, 0, 0) or maybe rgb = (127, 0, 0), depending on rounding.

Instead I get (187, 0, 0).

Now I have two questions:

1. What is the rationale for this surprising behaviour? Other graphics software I have checked give me the result I expect, Photoshop does not.

2. The import one: Can I configure Photoshop to handle transparency the way I expect it to? So that the resulting color is determined by the "obvious" formula

    result = ((255 - alpha) * base + alpha * top) / 255 ?