I just built a desktop and put it upstairs in my room and I now have to setup the internet. I already have a family desktop downstairs which is connected to the modem and router. Instead of getting another router for my computer, I decided to install a wifi adapter in my computer (1st link). I am thinking that it will connect to the router wirelessly downstairs to get internet up to my new computer. My question is will this work, or am I thinking of something completely different. If needed here is my build (2nd link). Thanks in advance 
http://www.newegg.com/Product/Product.aspx?Item=N82E16833166073
http://pcpartpicker.com/p/zrx8t6

http://www.newegg.com/Product/Product.aspx?Item=N82E16833166073
http://pcpartpicker.com/p/zrx8t6