Multiplication Of Number Bases That Are Not Binary

Multiplication of number bases that are NOT binary, or numbers from base 3 upward, follow the same steps as the multiplication of binary numbers.

In this lesson, you will learn step-by-step method for the multiplication of number bases that are not binary.

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

Question on multiplication of number bases that are not binary

Let’s take an example:

Question:

Multiply 3145 by 245

STEP 1.

Position the numbers

Arrange the numbers the same way you would arrange them in your normal multiplication.

WORKINGEXPLANATION
3145
×245
______
You can decide not to include the base beside the numbers but remember the base for the steps below.

STEP 2.

Start your multiplication

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

WORKINGEXPLANATION
314
×24
_____
___1
4 × 4 = 16

The answer 16 is bigger than our base 5, so we use repeated division to break 16 down to (3, 1).

Write down the last digit (1) and carry (3) over to the next multiplication.

STEP 3.

Continue your multiplication

WORKINGEXPLANATION
31³4
× 2 4
______
___21
4 × 1 = 4
4 + 3 (carried over) = 7

The answer 7 is bigger than our base 5, so we use repeated division to break 7 down to (1, 2).

Write down the last digit (2) and carry (1) over to the next multiplication.

STEP 4.

Finish your multiplication with the 1st number

WORKINGEXPLANATION
3¹14
× 2 4
______
2321
4 × 3 = 12
12 + 1 (carried over) = 13

The answer 13 is bigger than our base 5, so we use repeated division to break 13 down to (2, 3).

Write down the entire number (2, 3) because there is no next multiplication to carry anything over to.

STEP 5.

Move to the 2nd number

WORKINGEXPLANATION
314
×24
______
2321
___3
2 × 4 = 8

The answer 8 is bigger than our base 5, so we use repeated division to break 8 down to (1, 3).

Write down the last digit (3) and carry (1) over to the next multiplication.

STEP 6.

Continue your multiplication

WORKINGEXPLANATION
31¹4
×2 4
______
,2321
__33
2 × 1 = 2
2 + 1 (carried over) = 3

The answer 3 is smaller than our number base 5, so there is no need for breaking it down.

STEP 7.

Finish your multiplication with the 2nd number

WORKINGEXPLANATION
314
×24
______
_,2321
1133
2 × 3 = 6

The answer 6 is bigger than our base 5, so we use repeated division to break 6 down to (1, 1).

Write down the entire number (1, 1) because there is no next multiplication to carry anything over to.

STEP 8.

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
314
×24
______
_,2¹3¹21
1 1 3 3
________
14 2 0 1
1 + nothing = 1

2 + 3 = 5
The answer 5 is equal to our base 5, so we break 5 down to (1, 0). Write 0, carry 1.

3 + 3 = 6 (+1) =7
The answer 7 is bigger than our base 5, so we break 7 down to (1, 2). Write 2, carry 1.

2 + 1 = 3 (+1) = 4

1 + nothing = 1

FINAL ANSWER:

3145 × 245

= 14201

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Otherwise,

Click the button to practice questions on number base.

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