Yes, but if you get into the details... The second stage of a bomb is the fusion in which a cylinder of hydrogen and/or lithium is encased by U-238. The primary stage, a trinity-like a-bomb, forces the cylinder to compress by its x-rays. The fusion reaction creates a bunch of energy, but more importantly a huge amount of neutrons. These neutrons cause the u-238 to undergo fission, which is responsible for a majority of the energy and pretty much all of the fallout.