Plot hole: For the supposed code that hacks into UK system, Sherlock deduces that the finger taps are counted as 1s in the binary code and the rest (while Moriarty's fingers are in the air) are taken as 0s. Sherlock can't know the rate at which the rests are counted in the binary code that he thinks Moriarty tapped out. So even if the key code was real, he wouldn't have known what it was.
Suggested correction: I think you could figure it out, assuming the rests are all approximately the same length, which is also similar to the tap length, which is how most people would intuitively try to tap a binary code. As there can only be whole numbers of 0s, there can't be that many possibilities for the code. Also, if Moriarty wanted Sherlock to find the code, he would have taken care to make it deducible.
