Multiplication of binary numbers, as with bases that are not binary, follows a method and a rule.

In this lesson, you will learn the step-by-step method and the rule to the multiplication of binary numbers.

BONUS:A link to practice questions on number bases is included at the end of this lesson.

## What are binary numbers?

Binary numbers are numbers in base two.

## Question on multiplication of binary numbers

Let’s take an example:

Question:Multiply 101

_{2}by 110_{2}

## STEP 1.

### Position the numbers

Arrange the numbers exactly how you would arrange them in your normal multiplication.

WORKING | EXPLANATION |

101_{2}110 _{2}______ | You can decide not to include the base beside the numbers but remember the base for subsequent steps below. |

## STEP 2.

### Start your multiplication

Start from the back as you would do in your normal multiplication.

WORKING | EXPLANATION |

10111 0_____ ___0 | 0 × 1 = 0 The answer 0 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 3.

### Continue your multiplication

WORKING | EXPLANATION |

10111 0_____ _,00 | 0 × 0 = 0 The answer 0 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 4.

### Finish your multiplication with the 1st number

WORKING | EXPLANATION |

10111 0______ 000 | 0 × 1 = 0 The answer 0 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 5.

### Move to the 2nd number

WORKING | EXPLANATION |

1011 10_____ 000 _,1 | 1 × 1 = 1 The answer 1 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 6.

### Continue your multiplication

WORKING | EXPLANATION |

1011 10_____ _000 _01 | 1 × 0 = 0 The answer 0 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 7.

### Finish your multiplication with the 2nd number

WORKING | EXPLANATION |

1011 10_____ _,000 101 | 1 × 1 = 1 The answer 1 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 8.

### Move to the 3rd number

WORKING | EXPLANATION |

101110_____ _,000 101 _,1 | 1 × 1 = 1 The answer 1 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 9.

### Continue your multiplication

WORKING | EXPLANATION |

101110_____ __,000 _101 _01 | 1 × 0 = 0 The answer 0 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 10.

### Finish your multiplication with the 3rd number

WORKING | EXPLANATION |

101110_____ ___000 _,101 101 | 1 × 1 = 1 The answer 1 is smaller than our number base 2, so there is no need for breaking it down. |

## STEP 11.

### Add your results together

After multiplying all the numbers, follow the steps in the addition of number base to add all your result together.

WORKING | EXPLANATION |

101110_____ ___000 _,101 101 _______ 11110 | 0 + nothing = 0 0 + 1 = 1 0 + 0 + 1 = 1 1 + 0 = 1 Nothing + 1 = 1 |

FINAL ANSWER:101

_{2}× 110_{2}=

11110_{2}

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