Chapter 6 Limited Quality of Arithmetic Operations
6.1 Precision of Number Representation
In the previous chapters, we concentrated on the representation of numbers and on the ways in which the processor performs the four basic arithmetic operations. The aim of this chapter is to make the reader aware of the problem of the finite precision of calculations, which increases with the number of arithmetic operations. It is particularly noticeable in iterative versions of numerical algorithms and in operations on large data structures, e.g. matrices. The causes of the mentioned imperfection are as follows:
- Limited width of a register or memory cell
- Inability to express exactly some numbers on a given basis, e.g. π, ...
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