# Binary, decimal, and hexadecimal conversions

## Binary

Computers work on the principle of number manipulation. Inside the computer, the numbers are represented in bits and bytes. For example, the number three is represented by a byte with bits 0 and 1 set to "00000011" which is a numbering system using base 2. People commonly use a decimal or Base 10 numbering system.

What this means is that, in Base 10, you count from 0 to 9 before adding another digit. For example, the number 22 in Base 10 means we have two sets of 10's and two sets of 1's.

**Base 2** is also known as **binary** since there can only be two values for a specific digit; either a 0 = OFF or a 1 = ON. You cannot have a number represented as 22 in binary notation. The decimal number 22 is represented in binary as 00010110. By following the below chart, that breaks down to:

Bit Position | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |

Decimal | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

22 or 00010110:

All numbers representing 0 are not counted, **128, 64, 32, 8, 1** because 0 represents OFF.

However, numbers representing 1 are counted, **16 + 4 + 2** = 22 because 1 represents ON.

### Decimal values and binary equivalents chart

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

1 | 1 |

2 | 10 |

3 | 11 |

4 | 100 |

5 | 101 |

6 | 110 |

7 | 111 |

8 | 1000 |

9 | 1001 |

10 | 1010 |

16 | 10000 |

32 | 100000 |

64 | 1000000 |

100 | 1100100 |

256 | 100000000 |

512 | 1000000000 |

1000 | 1111101000 |

1024 | 10000000000 |

## Hexadecimal

Another numbering system used by computers is hexadecimal (hex), or Base 16. In this system, the numbers are counted from 0 to 9, then letters A to F, before adding another digit. The letters A through F represent decimal numbers 10 through 15, respectively. The below chart indicates the values of the hexadecimal position compared to 16 raised to a power and decimal values. It's easier to work with large numbers using hexadecimal values than decimal.

To convert a value from hexadecimal to binary, you translate each hexadecimal digit into its 4-bit binary equivalent. Hexadecimal numbers have either a *0x* prefix or an *h* suffix.

For example, consider the hexadecimal number:

0x3F7A

Using the Binary chart and the Hex chart below, this translates into the binary value:

0011 1111 0111 1010

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

0 | 0 | 0000 |

1 | 1 | 0001 |

2 | 2 | 0010 |

3 | 3 | 0011 |

4 | 4 | 0100 |

5 | 5 | 0101 |

6 | 6 | 0110 |

7 | 7 | 0111 |

8 | 8 | 1000 |

9 | 9 | 1001 |

10 | A | 1010 |

11 | B | 1011 |

12 | C | 1100 |

13 | D | 1101 |

14 | E | 1110 |

15 | F | 1111 |