Numbers - Mathematics for Computer Graphics - page 5

2
Numbers

All sorts of number system have been proposed by previous civilizations, but
our current system is a positional number system using a base 10. The number
1234 really means the sum of one thousand, plus two hundreds, plus three tens,
plus four ones, which can be expressed as 1 1. It

should be obvious that the base 10 is nothing special, it just so happens that
human beings have evolved with 10 digits, which we use for counting. This
suggests that any number can be used as a base: 2, 3, 4, 5, 6, 7, etc. In fact,
the decimal number system is not very convenient for computer technology,
where electronic circuits switch on and off billions of times a second using
binary numbers - numbers to a base 2 - with great ease. In this text there is
no real need to explore such numbers. This can be left to programmers who
have to master number systems such as binary (base 2), octal (base 8) and
hexadecimal (base 16).
The only features of numbers we have to revise in this chapter are the
families of numbers that exist, what they are used for, and any problems
that arise when they are stored in a computer. Let's begin with the natural
numbers.

× 1000 + 2 × 100 + 3 × 10 + 4 ×

2.1 Natural Numbers

The natural numbers are used for counting, ordering and

labelling. Note that negative numbers are not included. We often use natural
numbers to subscript a quantity to distinguish one element from another, e.g.
x 1 ,x 2 ,x 3 ,x 4 ,...

{ 0 , 1 , 2 , 3 , 4 ,... }