Cheat Engine

[Zanzer]

You can set your address entry type to binary and tell it how many bits you want to display.
After you change it to binary, you can right-click the entry and select Show as binary.
So you can do your bit manipulations directly within CE, instead of Calculator.

Just want to add to your description and state that each bit likely represents a specific skull, not just any old skull.
The first bit likely represents the skull found on the first level. The second bit is the skull on the second level. etc.
This means if you missed the first skull and got the second, your 4-byte address would be a 2 (binary 0010).

I assume you can replay a level and this lets the game know that you already have the skull on level 2.
That way it doesn't just let you get the skull on level 2 twice to increase your bits to (0011).