Maximum number of DS18B20 on one pin

These gadgets each have a 48 bit address. Every device that comes from their factory allegedly has a unique 48 bit ID. That is billions of ID numbers.

If you have, say, 10 ( or 50 ) devices on your network, the first thing you have to do is find out what the numbers of your 10 ( or 50 ) devices are. Your master device ( ie. your arduino ), has to look for all of the BILLIONS of 48 bit addresses, and notice which 10 of those possible billions of addresses responds. Once it has those 10 ( or 50 ) addresses, it keeps them in a table and only tries to talk to those specific addresses.

Suppose you have a cell phone and 50 friends and you lost all your friends number. You could dial ALL THE CELL PHONES IN THE WORLD and ask them if they are your friend, and then write down the numbers of the 50 that you find. This would be an impractical process. Fortunately, they have a slightly smarter scheme, but it still takes a fairly long time. They use subsets of the 48 bit addresses to save time.