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.
| WORKINGS | EXPLANATION |
| 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.
| WORKINGS | EXPLANATION |
| 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
| WORKINGS | EXPLANATION |
| 31¹4 +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
| WORKINGS | EXPLANATION |
| 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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