### Table of Contents

# Units explained

In several places in this website, units which measure various things are mentioned, this page will try to explain them.

## Bits

The smallest unit of measuring data storage is a **bit**.

One bit can be either on or off, commonly represented by a `1`

or a `0`

. This corresponds to a voltage being present or absent.

## Bytes, Kilobytes, Megabytes, Gigabytes and Terabytes.

One Byte is composed of 8 bits. Why 8 bits and not 10? Data in computers is counted in what is referred to as Binary which just used 1's and 0's to count with. This might seem confusing, but as computers are electrical and electricity can be either on or off, it is convenient to use.

Binary numbering is called base-2 meaning we carry over in powers of 2. So the sequence of numbers in binary is 1, 2, 4, 8, 16, 32. 10 is missed out of the sequence.

Normal counting uses numbers 0 to 9 and is called denary, sometimes also called base-10. Humans probably started to count in multiples of 10 because we have 10 digits between two hands.

Compared to binary, the sequence of denary numbers is 1, 10, 100, 1000, 10000.

Sometimes four bits are combined together and called a `nibble`

. likewise two bytes together are sometimes called a `word`

and two words are called a `long word`

.

A thousand Bytes are called a Kilobyte (the same as 1000 metres are called a kilometre) but because it is a “binary 1000”, one Kilobyte is actually 1024 bytes.

A thousand Kilobytes (or a million Bytes) are called a Megabyte, if we had a very long road which was 1000 Kilometres long, it could be called a Megametre. As with Kilobytes, a Megabyte is actually 1024 Kilobytes.

There is a pattern here, the next unit, a Gigabyte is 1024 Megabytes, and going up again, we have a Terabyte which is 1024 Gigabytes.

## Binary Explained

### Denary counting

When we count in real life, we count in multiples of 10, so we start at 1 and count to 10 and then add start again. Actually we should start at 0 and count to 9, so the next number is 10. 0-9 are single digits, but 10 is two digits. As we count another 10, we change the 1 to a 2, and the same with 2 to a 3 for thirty. When we reach 99, the next jump adds a third digit and becomes 100.

This is known as Denary maths (Middle English from Latin, originally, adjective, containing ten from deni, from New World Dictionary).

The table below shows this a different way. In the first example there are the same number of number, it doesn't matter if we start from 0 or 1.

Counting from 1 to 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Counting from 0 to 9 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

This table shows how we keep adding 1 and how we carry over when we reach 9, reading down from left to right.

0 | 10 | 20 | 30 | .. | 90 | 100 | 110 | 120 |

1 | 11 | 21 | 31 | .. | 91 | 101 | 111 | 121 |

2 | 12 | 22 | 32 | .. | 92 | 102 | 112 | 122 |

. | .. | .. | .. | .. | .. | … | … | … |

8 | 18 | 28 | 38 | .. | 98 | 108 | 118 | 128 |

9 | 19 | 29 | 39 | .. | 99 | 109 | 119 | 129 |

### Binary counting

Binary maths works the same way, but we just have 0 and 1. The first binary number is 0b (zero denary), the second is 1b (one denary),the next number after 1b is 10b (two denary). I have used a “b” after the numbers here to show they are binary numbers and not denary.

This table shows how binary counting works, again reading down from left to right.

00 | 10 | 100 | 110 | 1000 | 1010 | 1100 | 1110 |

01 | 11 | 101 | 111 | 1001 | 1011 | 1101 | 1111 |

These numbers correspond to

Denary | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

Binary | 00 | 01 | 10 | 11 | 100 | 101 | 110 | 111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |