When we work with computers, one of the first things we will need is **to store integers***(and that was needed back in the day)*.

Remember that integers include:

**Positive natural numbers***(1, 2, 3…)***Zero***(0, here a zero, look how nice, all round)***Negative numbers***(-1, -2, -3…)*

But as we know, internally **our computer only knows numbers in binary system**. So we will have to see how we can represent our numbers in this system.

For now, in this article we will see **how to encode positive integers and zero** *(in the next article we will talk about negative numbers)*.

## Representation of positive integers in binary

The representation of * positive integers is the simplest of all*. It really doesn’t have much mystery, it’s simply counting upwards

*(it doesn’t matter if it’s Base 2, Base 10, or Base “whatever”)*.

But let’s write it down in some guidelines:

- Zero is zero, in any base
- From there, we increment based on the base we are working with

For example, here are the first 16 positive numbers represented, counting zero, represented in Decimal and Binary systems:

Decimal | Binary |
---|---|

0 | 0000 |

1 | 0001 |

2 | 0010 |

3 | 0011 |

4 | 0100 |

5 | 0101 |

6 | 0110 |

7 | 0111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

11 | 1011 |

12 | 1100 |

13 | 1101 |

14 | 1110 |

15 | 1111 |

To change from one to the other we just have to change the base, as we saw in this article.

## How much is a binary number worth?

Importantly, I want to make a reflection that I will not tire of repeating. * Do not confuse a number with its representation*.

I repeat this a lot because, if you understand that, you will avoid many problems and mistakes in understanding all of this

When you see a number in binary system, for example:

`10011001`

How much is that set of bits worth? You don’t know, **it means nothing until you tell me what it represents**.

So, it will be different things if:

- It represents an integer
- It represents a number with positives and negatives
- It represents a fractional number
- It represents something else …

That said, if you don’t tell me anything, the logical assumption is that **you are referring to a positive number, because it’s the simplest**. So the previous number is worth 153, if you don’t tell me anything else.