# Number system

## Introduction and notation

In a Number system of base N, there are N basic symbols (or digits) that correspond to the first N natural numbers including zero. To generate the rest of the numbers, the position of the symbol in the figure is used. The symbol in the last position has its own value, and as it moves to the left its value is multiplied by N.

If a text (such as this one) discusses multiple bases, and if ambiguity exists, the base is added in subscript to the right of the number, like this: numberbase. Numbers without subscript are considered to be decimal.

## The binary system

The most basic system is the binary system, N=2, so there are two symbols, 0 and 1. The binary number 101102 means 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20 = 2210 (in the familiar decimal notation).

Non-integers can be represented by using negative powers, which are set off from the other digits by means of a radix point (called a decimal point in base 10). The binary number 11.012 thus means 1 x 21 + 1 × 20 + 0 × 2-1 + 1 × 2-2 which equals 3.2510.