As others have said, an inflatable pad goes inside. The next best place is right under the top flap. The 3rd best place is strapped to the very top, if your pack already has two straps up there.

As for strapping anything to the exterior, I have found webbing straps to be the most convenient. You can make your own, or buy a ready made set at most outdoor stores. Tying it with cordage works as well, but you will need to learn the truckers hitch. I have used bungee in the past. Sometimes it plain didn't work very well. Other times it was perfect. I also have gotten some good bruises by using bungee.
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