A processing system always involves: (1) something to be processed; (2) a set of components that do the processing; and (3) a way to connect these components into a system. Digital systems process information. Therefore we should be able to identify all three of these things. Knowing them provides a clear idea of the nature of digital systems.
WHAT IS PROCESSED: BITS
To say that digital systems process information is elliptical, for information only exists in so far as it is represented in some physical form. Digital systems actually process these physical representations of information. Furthermore, the representations it uses are highly specific: they consist of sequences of bits.
Something represents a bit if it can take on just one of two possible values, which are usually called zero (0) and one (1). Thus, if we had something (we might as well call it a register, which is what we will call it eventually) that can represent (hold) a sequence of seven bits, then it could take on various values, such as:
In fact, the register could take on any of 2|^7 distinct patterns (where a^b is used to indicate that a is raised to the b power) corresponding to each bit-place taking on the value of 0 or 1 independently of the others. Thus, a seven bit register can represent one of 128 different situations (128 = 2^7).
The representation of digital information is always in sequences of digital bits. All information must somehow be encode into such sequences. That can be a problem. If you want to. encode the age of a man in years; then you have to decide what pattern is 0 years old (i.e., less than a year), what pattern is 1 year old, what pattern 2, and so on. We could adopt the following code:
You may recognize this as the standard way of encoding the integers into a binary sequence. It is normally referred to as the binary number system. It takes seven bits to hold all the possible ages of modern man; a sequence of only six bits would have only permitted ages through 63. The integer value is just