# Counting in Binary

Binary (base-two) numbers are only made of 0s and 1s. Counting in binary is similar to counting decimal (base-ten) numbers, that is one of the most popular numeral systems.

Binary (base-two) numbers are only made of 0s and 1s. Counting in binary is similar to counting decimal (base-ten) numbers, that is one of the most popular numeral systems. Let's explore these two systems:

**Decimal**

Instruction | Result |
---|---|

Start at 0 | 0 |

Count 1, 2, 3, 4, 5, 6, 7, 8, 9 | 9 |

Turn the 9 into a 0 adding 1 to the left | 10 |

Count up to 99 | 99 |

Turn the 00 into 00 adding 1 to the left | 100 |

In **binary** since it moves much quicker:

Instruction | Result | |
---|---|---|

Start at 0 | 0 | |

Add 1 | 1 | |

Turn 1 to 0 and add 1 to the left | 10 | |

Add 1 | 11 | |

Turn 11 into 00 adding 1 to the left | 100 | |

Add 1 | 101 | |

Turn 1 into 0 and add 1 to the left | 110 | |

Add 1 | 111 | |

Turn 111 to 000 and add 1 to the left | 1000 | |

Add 1 | 1001 |

The ASCII (American Standard Code for Information Interchange) character code chart demonstrates the equivalency between these two systems, using an 8-bit system:

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

0 | 00000000 | |

1 | 00000001 | |

2 | 00000010 | |

3 | 00000011 | |

4 | 00000100 | |

5 | 00000101 | |

6 | 00000110 | |

7 | 00000111 | |

8 | 00001000 | |

9 | 00001001 | |

10 | 00001010 | |

11 | 00001011 | |

12 | 00001100 | |

13 | 00001101 | |

14 | 00001110 | |

15 | 00001111 | |

16 | 00010000 | |

17 | 00010001 | |

18 | 00010010 | |

19 | 00010011 | |

20 | 00010100 | |

21 | 00010101 | |

22 | 00010110 | |

23 | 00010111 | |

24 | 00011000 | |

25 | 00011001 | |

26 | 00011010 | |

27 | 00011011 | |

28 | 00011100 | |

29 | 00011101 | |

30 | 00011110 | |

31 | 00011111 |

Every time we add a 1 to the left, the number gets doubled. Using a binary number of 10011011 as an example, if we break it down it gives us the following:

Digit | Multiplier |
---|---|

1 | 128 |

0 | 64 |

0 | 32 |

1 | 16 |

1 | 8 |

0 | 4 |

1 | 2 |

1 | 1 |

If we multiply each digit by its multiplier, we get 155.

If you use all the rules you have learned in this note, you can count binary up to 31 with one of your hands. With both hands you count up to 1,023. This is useful if you are trying to count big numbers and don't have a pen, paper or any device with a calculator. The following video shows how to count up to 31 in binary using your hands:

This note was inspired by a project I worked on called Binary Clock, where I use binary to count time.

## References

- “ASCII Table - ASCII Codes,Hex,Decimal,Binary,Html.” Accessed September 30, 2021. https://www.rapidtables.com/code/text/ascii-table.html.
- “Binary Fingers!” Accessed October 1, 2021. https://www.mathsisfun.com/numbers/binary-count-fingers.html.
- “Binary Number System.” Accessed September 30, 2021. https://www.mathsisfun.com/binary-number-system.html.
- “Binary-Clock.” Accessed September 30, 2021. https://binary-clock.org/.
- “Decimal.” In
*Wikipedia*, September 17, 2021. https://en.wikipedia.org/w/index.php?title=Decimal&oldid=1044840857. - Techquickie.
*Binary Numbers and Base Systems as Fast as Possible*, 2014. https://www.youtube.com/watch?v=LpuPe81bc2w. - Transformers And Power Rangers Toy Reviews.
*How to Count to 31 on One Hand by Using the Binary Counting System*, 2012. https://www.youtube.com/watch?v=Bke95oWWZII.