# Number SystemsBase Conversion

Base conversion lets you convert the same number between its different number representation systems. Base conversions are used all in many different ways in computer science.

## Why is Base Conversion important

It's important to understand that you can represent the same number in multiple ways. Consider the two number systems, **decimal** and **binary**. In decimal, the number `5`

is represented by `5`

In binary, the number `5`

is represented by `101`

The decimal number system is used because it's how humans broadly know how to interact with numbers.

The binary number system is the number system used for all computing systems to store/access/manipulate information.

We need to know how to convert between number systems because real world systems have different constraints.

**Example:** a user inputs a number on a form in the **decimal **system, our computer then converts that number into the **binary** number system so we can store it on our computer.

## Common base types

**Base2- Binary -** Used extensively by computers to store, access and manipulate data directed to and from a CPU

**Base10 - Decimal** - The standard human readable number system

**Base16 - Hexadecimal**. Used extensively in assembly programming and referencing memory addresses

**Base32 -** a case insensitive way to encode strings like in DNS names

**Base64** - A case sensitive way to represent a significant amount of numbers in shorter string

## How many numbers are represented by each

There is a simple formula for calculating how many numbers can be represented by a set of digits in a given number system.
`{Numbers that can be represented} = {base}^{number of digits}`