In the new model of Apple TV, the company from Cupertino said that it has implemented a single core processor and not a dual core one like the rest of the terminals in which the same chip is mounted. Although everyone assumed that Apple designed a new processor, in reality the A5 chip in the new Apple TV it's built based on the A5 chip in the iPhone 4S and iPad 2. The component in the Apple TV is smaller, it is built using a 32 nm manufacturing process and is based on the dual-core processor found in other iDevices.
Either Apple is only using one core or they are binning parts. Parts binning is a common process in semiconductors where devices are segregated (binned) based on meeting a subset of the overall requirements, in this case they could disable the bad core, this increases the usable die per wafer, lowering the cost.
No one knows what Apple did to offer a single-core processor, but it is speculated that one of the two processors of the A5 chip would have been disabled or that Apple would have given up on implementing one in its chip. No matter how Apple thought everything, the new processor works as well as possible, it can play movies in 1080p format without the slightest problem, although the iPhone 4S can't really do the same with any kind of movies available in the same format.
