@kingpin3690: You can also buy a 2nd or 3rd gen i3 (any i3) since i3 cpu have 4 threads and games recognize it as a quad core cpu. Games for which 4 core cpu are mandatory run on i3 cpu without any problems. But buy an i3 only if you feel fallout 4 is giving problems , which most probably wont happen.
@kingpin3690: You should run fine, you might turn down cpu intensive graphics options such as field of view. Your gpu is more than sufficient. At high settings (not ultra) you should get 45 fps
@streamline: Just buy a gtx750ti you can find one for 120$ at am@zon or 100$ if you are lucky. Its equally powerful as 7870 and will run on your existing power supply unlike the 7870. Make sure you are buying the 750 "ti" version.
@Gamer_4_Fun: Many people run their pc as a multitasking machine, the os takes around 1gb, if a web browser is also running then it might even eat up 2-4 gb ram. In a console 5 gb ram is available to games and 2 gb vram (amd hardware limitation). That means their pc version is a superior version and not a cheap port if it asks for "16 gb recommended" . They are just playing safe. We all know the game will hardly eat 4gb ram
srimasis' comments