Data Representation, Number Systems and Arithmetic Processes

Abstract

The basic concepts of digital computers have been introduced in the first two chapters in a largely descriptive way. In this chapter and the next, the fundamental techniques necessary to construct a working computer to implement the concepts discussed are presented. The importance of the binary technique has been stressed as a practical method of achieving the inherent speed and accuracy by removing tight tolerances from the actual voltage levels used by the electronics. The representation of non-numeric data, such as alphabetic characters, is also important. This chapter reviews the commonly used techniques.

Having established the concept of binary representation of information, then the manipulation of binary data can be treated as a logical two-state process — for example, on or off, open or shut, true or false. For simplicity the two logical states are represented as 0 or 1, drawing an immediate parallel with binary numbers. Indeed it is shown in some detail in the next chapter how logic circuits are used to implement binary arithmetic units, such as an adder.