Alan Turing realized that there was no fundamental difference between the mechanical operations computers perform and thinking. Children of init are processes that are created when you disconnect without logging out. The process id number of their parent is set to 1 and they are detached. This means that whatever work they do cannot be utilized by the user since there is no way of attaching them. So the only thing that children of init do is waste system resources till someone finds them running and kills them.
Binary information is just a type of digital information.
Digital information refers to any electronically stored information which is represented using a finite number of states or symbols. Binary information refers to digital information that is represented using 2 symbols. These could be 0's and 1's, on's and off's, true and false or any other scheme where there are only 2 possibilities. The first alphabet was developed around 2000 BC by the Phoenicians. Babbage underestimated the cost of his computers because he had no idea and experience about the complexity of the machines he wanted to build.