Addition Of Number Bases That Are Not Binary

Addition of number bases that are not binary, or numbers from base 3 upward, follow the same method as with the addition of binary numbers.

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

Let’s take an example:

QUESTION:

Add 3145 and 245

STEP 1.

Position the numbers

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

WORKINGSEXPLANATION
3145
+245
______
You can decide not to include the base beside the numbers but remember the base for subsequent steps below.

STEP 2.

Start your addition

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

WORKINGSEXPLANATION
314
+24
_____
___3
4 + 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 addition.

STEP 3.

Continue your addition

WORKINGSEXPLANATION
34
+2 4
_____
_,4 3
1 + 2 = 3
3 + 1 (carried over) = 4

The answer 4 is smaller than our base 5, so there is no need for breaking it down.

STEP 4 — final answer

Finish your addition

WORKINGSEXPLANATION
314
+24
_____
343
3 + nothing = 3

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

FINAL ANSWER:

3145 + 245

= 3435

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Otherwise,

Click the button to practice questions on number base.

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