Multiplication Of Binary Numbers

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 1012 by 1102

STEP 1.

Position the numbers

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

WORKINGEXPLANATION
1012
1102
______
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.

WORKINGEXPLANATION
101
110
_____
___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

WORKINGEXPLANATION
101
110
_____
_,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

WORKINGEXPLANATION
101
110
______
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

WORKINGEXPLANATION
101
110
_____
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

WORKINGEXPLANATION
101
110
_____
_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

WORKINGEXPLANATION
101
110
_____
_,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

WORKINGEXPLANATION
101
110
_____
_,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

WORKINGEXPLANATION
101
110
_____
__,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

WORKINGEXPLANATION
101
110
_____
___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.

WORKINGEXPLANATION
101
110
_____
___000
_,101
101
_______
11110
0 + nothing = 0

0 + 1 = 1

0 + 0 + 1 = 1

1 + 0 = 1

Nothing + 1 = 1

FINAL ANSWER:

1012 × 1102

= 111102

Do you have something to ADD TO or ASK ON this topic? Comment below and a Teacher or fellow TOPPER will reply you.

Otherwise,

Click the button to practice questions on number base.

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