# Binary Adding, Subtraction, Multiplicaton and Division

## Adding, subtracting, multiplying and dividing binary numbers

A binary signal or number is one that can take only one value: *1 or 0* -or *on or off*.

### Addition Binary Numbers

Rule to follow when binary numbers are added:

*0 + 0 = 0**0 + 1 = 1**1 + 0 = 1**1 + 1 = 0 (with a carry of 1)*

#### Example - Adding Binary and Decimal Numbers

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

5 + 6 = 11 | 101 + 110 = 1011 |

15 + 20 = 35 | 1111 + 10100 = 100011 |

3.25 + 5.75 = 9.00 | 11.01 + 101.11 = 1001.00 |

### Subtracting Binary Numbers

Rule to follow when binary numbers are subtracted:

*0 - 0 = 0**1 - 0 = 1**1 - 1 = 0**0 - 1 = 1 (with a borrow of 1)*

#### Example - Subtracting Binary and Decimal Numbers

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

9 - 5 = 4 | 1001 - 101 = 0100 |

16 - 3 = 13 | 10000 - 11 = 01101 |

6.25 - 4.50 = 1.75 | 110.01 - 100.10 = 001.11 |

### Multiplication of Binary Numbers

Rule to follow when binary numbers are multiplied:

*0 x 0 = 0**0 x 1 = 0**1 x 0 = 0**1 x 1 = 1*

### Division of Binary Numbers

Rule to follow when binary numbers are divided:

*0 / 1 = 0**1 / 1 = 1*