Computers use switches to store and process data. These switches are either *on* or *off* — like the light switch in your bedroom is either on or off. The switches are therefore described as being **binary**: one of only two possible states. If you walked into your room and someone had removed the lightbulb (or you were blindfolded) you would be able to work out from the position of the light switch whether the light was on or off.

## 1. Represent

You have been using a numbering system from an early age. But did you know that it has a name? Or that it is not the *only* numbering system?

Microsoft Excel has several functions to work with *decimal*, *binary* and *hexadecimal* number representations. See Excel’s DEC2BIN function.

- Denary
- The number system most commonly used by people. It contains 10 unique digits 0 to 9. Also known as
*decimal*or*base 10*. - Binary
- A number system that contains two symbols, 0 and 1. Also known as
*base 2*. The “least significant bit” is on the right — you start the notation from the right (as we do in decimal).

## 2. Bit

**Bit** is short for “**bi**nary digi**t**”. Binary (or *base-2*) is a numeric system that only uses two digits — 0 and 1.

A single binary digit can only represent `True (1)`

or `False (0)`

— we refer to these as **Boolean** values.

These state values are commonly represented as either a `1`

or `0`

.

Computers operate using binary, meaning they store data and perform calculations using **only** zeros and ones!

## 3. Byte

The **byte** is a unit of digital information that consists of 8 bits. Historically, the *byte* was the number of *bits* used to encode a single character of text in a computer. For this reason, it is the *smallest addressable unit of memory* in many computer architectures.

## 4. Binary

The characters we use are represented in *binary* as follows:

Character | ASCII ^{[2]} | Binary representation ^{[1]} |
---|---|---|

F | 70 | 01100110 |

o | 111 | 01101111 |

x | 120 | 01111000 |

0 | 48 | 00110000 |

1 | 49 | 00110001 |

2 | 50 | 00110010 |

3 | 51 | 00110011 |

A | 65 | 01000001 |

B | 66 | 01000010 |

C | 67 | 01000011 |

a | 97 | 01100001 |

b | 98 | 01100010 |

c | 99 | 01100011 |

## 5. Units

1 Bit

1 Byte = 8 Bits

1 Kilobyte = 1024 Bytes

Megabyte = 1024 Kilobytes

Gigabyte = 1024 Megabytes

Terabyte = 1024 Gigabytes

Petabyte = 1024 Terabytes

Exabyte = 1024 Petabytes

Zettabyte = 1024 Exabytes

Yottabyte = 1024 Zettabytes

#### References:

*Binary to Decimal converter*(no date)*Binary to Decimal Converter*. Available at: https://www.rapidtables.com/convert/number/binary-to-decimal.html (Accessed: 20 October 2023).*ASCII Table*(no date)*ASCII Table – ASCII Character Codes, HTML, Octal, Hex, Decimal*. Available at: https://www.asciitable.com/ (Accessed: 20 October 2023).