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## Chapter 15. Arithmetic and Arbitrary-Precision Arithmetic with gawk

This chapter introduces some basic concepts relating to how computers do arithmetic and defines some important terms. It then proceeds to describe floating-point arithmetic, which is what `awk` uses for all its computations, including a discussion of arbitrary-precision floating-point arithmetic, which is a feature available only in `gawk`. It continues on to present arbitrary-precision integers, and concludes with a description of some points where `gawk` and the POSIX standard are not quite in agreement.

### Note

Most users of `gawk` can safely skip this chapter. But if you want to do scientific calculations with `gawk`, this is the place to be.

## A General Description of Computer Arithmetic

Until now, we have worked with data as either numbers or strings. Ultimately, however, computers represent everything in terms of binary digits, or bits. A decimal digit can take on any of 10 values: zero through nine. A binary digit can take on any of two values, zero or one. Using binary, computers (and computer software) can represent and manipulate numerical and character data. In general, the more bits you can use to represent a particular thing, the greater the range of possible values it can take on.

Modern computers support at least two, and often more, ways to do arithmetic. Each kind of arithmetic uses a different representation (organization of the bits) for the numbers. The kinds of arithmetic that interest us are:

Decimal arithmetic ...

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