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Number Systems Overview

Two different hands holding a strip of paper with binary numbers on it. Source: Microsoft.

What is a Number System?

Human nature dictates that we try to quantify everything we come in contact with, e.g. the number of students in a class, the number of eggs in a basket, etc. If we think about the type of things humans try to quantify, we can see that they are not all quantified in the same units of measure, e.g. time is measured in hours, minutes and seconds but the distance from Glasgow to Edinburgh is measured in miles. Therefore, a number system defines a set of values used to represent a quantity. Number Systems can be traced back to the early civilisations of Egypt and Babylon. These cultures could perform arithmetic operations on whole numbers, i.e. numbers without a decimal point.

There are many number systems that have been, and still are in use, some of which may be familiar, these include Arabic, Babylonian, Mayan and Roman. The Roman number system uses numerals to represent each number, e.g. the number 5 is represented as V. In contrast, the most commonly used system is the Arabic system which uses the digits 0 to 9. This number system was used as early as the 3rd Century BC.

Each number system can be defined by its base (sometimes referred to as the radix). This base value of the number system indicates the number of different values the set has before repeating itself, e.g. Decimal has a base of ten values, hence, the digits 0-9, Octal has a base of 8 values, hence the digits 0-7.

Next: Common Number Systems