# Visual Maths: Number System

Imagine a machine which is nothing more than a row of boxes that extends as far to the left. Let’s call it a “two-one machine” both written and read in a funny backwards way.

And what do you do with this machine? You put in dots. Dots always go into the rightmost box.

- Put in one dot, and, well, nothing happens: it stays there as one dot.
- But put in a second dot – always in the rightmost box – and then something exciting happens. Whenever there are two dots in a box they explode and disappear – Bhoom! – to be replaced by one dot, one box to the left.

We see that two dots placed into the machine yields one dot followed by zero dots.

Putting in a third dot – always the rightmost box – gives the picture one dot followed by one dot.

Let’s make a table and do it for all numbers till 10

Numbers | 1 <- 2 |
---|---|

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

Here is a visual way to look at it

Now, instead of playing with a 1 <- 2 machine, we could play with a 1 <- 3 machine (again

written and read backwards, a “three-one “machine). Now whenever there are three dots in a

box, they explode away to be replaced with one dot, one box to the left.

Numbers | 1 <- 3 |
---|---|

1 | 1 |

2 | 2 |

3 | 10 |

4 | 11 |

5 | 12 |

6 | 20 |

7 | 21 |

8 | 22 |

9 | 100 |

10 | 101 |

You can try this for different types of machine: 1 <- 4, 1 <- 5 and so on…

**What are these machines doing?**

Can you figure out what these machines are actually doing? Why is the code for two hundred and seventy-three in a 1 <- 10 machine, “273”? Are all the codes for numbers in a 1 <- 10 sure to be identical to how we normally write numbers. If you can answer that question, can you then also make sense of all the codes for a 1 <- 2 machine? What does the code 1101 for the number thirteen mean?

Both the above approaches, teaches the concept of binary (1 <-2) , tertiary (1 <- 3) and decimal (1 <- 10) number systems.