The Universe of Binary Numbers
Our main goal in this chapter is to stimulate reasoning by analogy and to show that the same concept can be viewed from several different perspectives. The material presented here is illustrated with a good number of examples. Some of the sections are very speculative, and may appear chaotic. Conversely, the rest of the sections follow a very strict organization. The choice depended on the type of material presented and discussed in each section. We start with an almost surprising question: what is a bit? Rather that define it, we introduce it by using Shannon’s amount of information theorem and then progress to a discussion of several different number bases. The circuit is used to represent the bit from a dynamic point of view (to be referred to later in the book in terms of bra-ket notation). We then focus on the basic concepts of binary logic, progressing to basic logic operations that can be performed through logic gates and focusing on special universal sets of gates with which we can do very many things. The chapter concludes with two applications: the Half Adder as a physical summing device, and a billiard game representation of a number of basic operations with bits.